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<h2>SL Paper 2</h2><div class="specification">
<p>A vertical wall carries a uniform positive charge on its surface. This produces a uniform horizontal electric field perpendicular to the wall. A small, positively-charged ball is suspended in equilibrium from the vertical wall by a thread of negligible mass.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The charge per unit area on the surface of the wall is<em> σ</em>. It can be shown that the electric field strength <em>E</em> due to the charge on the wall is given by the equation</p>
<p style="text-align:center;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mi>σ</mi><mrow><mn>2</mn><msub><mi>ε</mi><mn>0</mn></msub></mrow></mfrac></math>.</p>
<p>Demonstrate that the units of the quantities in this equation are consistent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.</p>
<p>Determine the horizontal force that acts on the ball.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The charge on the ball is 1.2 × 10<sup>−6 </sup>C. Determine <em>σ</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The centre of the ball, still carrying a charge of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mtext>C</mtext></math>, is now placed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>40</mn><mo> </mo><mtext>m</mtext></math> from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.</p>
<p>P is the point on the line joining the charges where the electric field strength is zero.<br>The distance PQ is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>22</mn><mo> </mo><mtext>m</mtext></math>.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Calculate the charge on Q. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>identifies units of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math> as <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>C</mi><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>×</mo><mfrac><mrow><mi>N</mi><msup><mi>m</mi><mn>2</mn></msup></mrow><msup><mi>C</mi><mn>2</mn></msup></mfrac></math> seen and reduced to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mtext>N C</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> <strong>✓</strong></p>
<p> </p>
<p><em>Accept any analysis (eg dimensional) that yields answer correctly</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>horizontal force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math> on the ball<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>T</mi><mo> </mo><mi>sin</mi><mo> </mo><mn>30</mn></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mi>m</mi><mi>g</mi></mrow><mrow><mi>cos</mi><mo> </mo><mn>30</mn></mrow></mfrac></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>«</mo><mo>=</mo><mi>m</mi><mi>g</mi><mo> </mo><mi>tan</mi><mo> </mo><mn>30</mn><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>×</mo><mi>tan</mi><mo> </mo><mn>30</mn><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>14</mn><mo> </mo><mo>«</mo><mtext>N</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em><br>Allow g = 10 N kg<sup>−1</sup></em></p>
<p><em>Award <strong>[3] marks</strong> for a bald correct answer.</em></p>
<p><em>Award <strong>[1max]</strong> for an answer of zero, interpreting that the horizontal force refers to the horizontal component of the net force.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>«</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup><mo>»</mo></math><strong> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>8</mn><mo>.</mo><mn>85</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>12</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>14</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfrac><mo>»</mo><mo>=</mo><mn>2</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><msup><mtext>C m</mtext><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math> <strong>✓</strong></p>
<p><em> <br>Allow <strong>ECF</strong> from the calculated F in (b)(i)</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>Q</mi><mrow><mn>0</mn><mo>.</mo><msup><mn>22</mn><mn>2</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>18</mn><mn>2</mn></msup></mrow></mfrac></math> ✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>+</mo><mo>»</mo><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><mo>«</mo><mtext>C</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p>2sf <strong>✓</strong></p>
<p><em><br>Do not award <strong>MP2</strong> if charge is negative </em></p>
<p><em>Any answer given to 2 sig figs scores <strong>MP3</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A charged particle, P, of charge +68 μC is fixed in space. A second particle, Q, of charge +0.25 μC is held at a distance of 48 cm from P and is then released.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The diagram shows two parallel wires X and Y that carry equal currents into the page.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Point Q is equidistant from the two wires. The magnetic field at Q due to wire X <strong>alone </strong>is 15 mT.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the force on Q at the instant it is released.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the motion of Q after release.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram draw an arrow to show the direction of the magnetic field at Q due to wire X <strong>alone</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the magnitude and direction of the resultant magnetic field at Q.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>5</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>25</mn></mrow></mfrac><mo>=</mo></math>» 18 «V» ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>68</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>48</mn><mn>2</mn></msup></mrow></mfrac></math> ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>66</mn></math> «N» ✓</p>
<p> </p>
<p><em>Award <strong>[2]</strong> marks for a bald correct answer. </em></p>
<p><em>Allow symbolic k in substitutions for <strong>MP1</strong>. </em></p>
<p><em>Do <strong>not</strong> allow <strong>ECF</strong> from incorrect or not squared distance.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Q moves to the right/away from P «along a straight line»</p>
<p><em><strong>OR</strong></em></p>
<p>Q is repelled from P ✓</p>
<p><br>with increasing speed/Q accelerates ✓</p>
<p>acceleration decreases ✓</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p> </p>
<p><img src="data:image/png;base64,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"></p>
<p>arrow of any length as shown ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«using components or Pythagoras to get» <em>B</em> = 21 «mT» ✓</p>
<p>directed «horizontally» to the right ✓</p>
<p> </p>
<p><em>If no unit seen, assume</em> mT.</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph shows how current <em>I</em> varies with potential difference <em>V</em> for a resistor R and a non-ohmic component T.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i) State how the resistance of T varies with the current going through T.</p>
<p>(ii) Deduce, without a numerical calculation, whether R <strong>or</strong> T has the greater resistance at <em>I</em>=0.40 A.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Components R and T are placed in a circuit. Both meters are ideal.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Slider Z of the potentiometer is moved from Y to X.</p>
<p>(i) State what happens to the magnitude of the current in the ammeter.</p>
<p>(ii) Estimate, with an explanation, the voltmeter reading when the ammeter reads 0.20 A.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i</p>
<p><em>R</em><sub><em>T</em></sub> decreases with increasing <em>I</em></p>
<p><em><strong>OR </strong></em></p>
<p><em>R</em><sub><em>T</em></sub> and<em> I</em> are negatively correlated</p>
<p><em>Must see reference to direction of change of current in first alternative.<br>Do not allow “inverse proportionality”. <br>May be worth noting any marks on graph relating to 7bii</em></p>
<p> </p>
<p>ii</p>
<p>at 0.4 A: <em>V</em><sub>R</sub> > <em>V</em><sub>T</sub> <em><strong>or</strong></em> <em>V</em><sub>R</sub>= 5.6 V and <em>V</em><sub>T</sub> = 5.3 V</p>
<p><em>Award <strong>[0]</strong> for a bald correct answer without deduction or with incorrect reasoning. </em></p>
<p><em>Ignore any references to graph gradients.</em></p>
<p>so R<sub>R</sub> >R<sub>T</sub> because <em>V = IR</em> / <em>V</em>∝ R «and <em>I</em> same for both»</p>
<p><em>Both elements must be present for MP2 to be awarded.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i</p>
<p>decreases<br><em><strong>OR<br></strong></em>becomes zero at X</p>
<p> </p>
<p>ii</p>
<p>realization that <em>V</em> is the same for R and T<br><em><strong>OR<br></strong></em>identifies that currents are 0.14 A and 0.06 A</p>
<p><em>Award <strong>[0]</strong> if pds 2.8 V and 3.7 V or 1.4 V and 2.6V are used in any way. Otherwise award <strong>[1 max]</strong> for a bald correct answer. Explanation expected.</em></p>
<p>2 V = 2 V OR 2.0 V</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A lighting system consists of two long metal rods with a potential difference maintained between them. Identical lamps can be connected between the rods as required.</p>
<p style="text-align: center;"><img 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"></p>
<p>The following data are available for the lamps when at their working temperature.</p>
<p> </p>
<p style="padding-left: 90px;">Lamp specifications 24 V, 5.0 W</p>
<p style="padding-left: 90px;">Power supply emf 24 V</p>
<p style="padding-left: 90px;">Power supply maximum current 8.0 A</p>
<p style="padding-left: 90px;">Length of each rod 12.5 m</p>
<p style="padding-left: 90px;">Resistivity of rod metal 7.2 × 10<sup>–7</sup> Ω m</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Each rod is to have a resistance no greater than 0.10 Ω. Calculate, in m, the minimum radius of each rod. Give your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One advantage of this system is that if one lamp fails then the other lamps in the circuit remain lit. Outline <strong>one</strong> other electrical advantage of this system compared to one in which the lamps are connected in series.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r = \sqrt {\frac{{\rho l}}{{\pi {\text{R}}}}} ">
<mi>r</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mi>ρ</mi>
<mi>l</mi>
</mrow>
<mrow>
<mi>π</mi>
<mrow>
<mtext>R</mtext>
</mrow>
</mrow>
</mfrac>
</msqrt>
</math></span> <em><strong>OR </strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{7.2 \times {{10}^{ - 7}} \times 12.5}}{{\pi \times 0.1}}} ">
<msqrt>
<mfrac>
<mrow>
<mn>7.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>12.5</mn>
</mrow>
<mrow>
<mi>π</mi>
<mo>×</mo>
<mn>0.1</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> ✔</p>
<p><em>r</em> = 5.352 × 10<sup>−3</sup> ✔</p>
<p>5.4 × 10<sup>−3 </sup>«m» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \frac{{7.2 \times {{10}^{ - 7}} \times 12.5}}{{0.1}}">
<mi>A</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>7.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>12.5</mn>
</mrow>
<mrow>
<mn>0.1</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p><em>r</em> = 5.352 × 10<sup>−3</sup> ✔</p>
<p>5.4 × 10<sup>−3 </sup>«m» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>current in lamp = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{{24}}">
<mfrac>
<mn>5</mn>
<mrow>
<mn>24</mn>
</mrow>
</mfrac>
</math></span> «= 0.21» «A»</p>
<p><em><strong>OR</strong></em></p>
<p><em>n</em> = 24 × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{8}{{5}}">
<mfrac>
<mn>8</mn>
<mrow>
<mn>5</mn>
</mrow>
</mfrac>
</math></span> ✔</p>
<p> </p>
<p>so «38.4 and therefore» 38 lamps ✔</p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>when adding more lamps in parallel the brightness stays the same ✔</p>
<p>when adding more lamps in parallel the pd across each remains the same/at the operating value/24 V ✔</p>
<p>when adding more lamps in parallel the current through each remains the same ✔</p>
<p>lamps can be controlled independently ✔</p>
<p>the pd across each bulb is larger in parallel ✔</p>
<p>the current in each bulb is greater in parallel ✔</p>
<p>lamps will be brighter in parallel than in series ✔</p>
<p>In parallel the pd across the lamps will be the operating value/24 V ✔</p>
<p> </p>
<p><em>Accept converse arguments for adding lamps in series:</em></p>
<p><em>when adding more lamps in series the brightness decreases</em></p>
<p><em>when adding more lamps in series the pd decreases</em></p>
<p><em>when adding more lamps in series the current decreases</em></p>
<p><em>lamps can’t be controlled independently</em></p>
<p><em>the pd across each bulb is smaller in series</em></p>
<p><em>the current in each bulb is smaller in series</em></p>
<p> </p>
<p><em>in series the pd across the lamps will less than the operating value/24 V</em></p>
<p><em>Do not accept statements that only compare the overall resistance of the combination of bulbs.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A possible decay of a lambda particle (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\Lambda ^0}">
<mrow>
<msup>
<mi mathvariant="normal">Λ<!-- Λ --></mi>
<mn>0</mn>
</msup>
</mrow>
</math></span>) is shown by the Feynman diagram.</p>
<p style="text-align: left;"><img 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DACrhYwEy3UDzJgO1UZM9aow7edLk6u/qxQeQSSR4BgInnakpq4WKDzSJtOBpx+0sUoVB2BeAt4T6ntSEe8cyU/BBBAIKECBBMJ5SdzBCIUsNaL6JSOtqq9m2giQk0uRyAyAb6PkflxNQIIOFKAYMKRzUahEUAAAQQQQAABBBBIvADBROLbgBIgMGQB78k2HQl/Ra0h58eFCCAQgkBnq9pOBl//JYRUOAUBBBBwhADBhCOaiUIiMIhAAbPHDCLEYQRiL2BmVyvIin0+5IAAAgjYSIBgwkaNQVEQCE/Aq+72Vh0N7yLORgCBmAscV3N7d8xzIQMEEEDADgIEE3ZoBcqAQIQCWYU5Gjvgt9mr7pYGbaqaJbNqpfX336u0qaFF3O5ECM/lySPQ1aAqT4o8VQ3q6qmVWa16uTwpRapqONWzd8AXqaOVU+gZ8DAHEEAAgWQUGPD2IxkrS50QSC6B8zrZ1qpOZakg36P0gSrXfVDP3l2pxvzv6nc+n3y+/6uOR0Zo600rtb3l44GuYj8CCIQtkK7s/PGSOnSk7ZSYXy1sQC5AAAEHClzqwDJTZAQQCEPA2/G23tgzXvN+kHsh4BimrBn/Uz/zhZEIpyLgcIGWlhY999xzGjlypJYvX+7w2lB8BBBAwD4CBBP2aQtKgkCYAsM0NidXWdoX9LpUzzX6yvSVWvn8a7pm1nB1Z/83zcjLCHoNBxFIFoH9+/erurraqs7ChQs1Z86cOFTNo8Kc0eLRfxyoyQIBBBIuwH/rEt4EFACBoQqkKj07VwWDXZ4+WQ/+eI+2ffH/6NVHv6Gb8q9QSsosVW1qUAsL3Q2mx3EHCpw7d041NTWaPHmyNm/erIqKCtXW1qqsrExpaWlxqNF45WcP2PEwDvmTBQIIIBA/AYKJ+FmTEwJRF0gdm6PCUGaiTM/TjLKleuJnHfL9oUMHX/2KTq68SdMf3dNrsGnUi0eCCMRVoL29XRs2bNCIESPU0dGhbdu2aePGjZoyZUpcy6GsXOWMHRbfPMkNAQQQSJAA3ZwSBE+2CERFIGOiZi34vI6Ek1hqlq4vW6xFv/iRthxp00mvlDHAzwpr1qxRdna2ZsyYYf0bTjaci0C8BI4cOaKXXnpJe/bsUXl5uU6fPq3MzMzwso/iGhFZC2aqaKAvVXil4mwEEEDA9gID3ELYvtwUEAEELIFMFc2apveaOwac5tXbskmzTLemmmMXzjFTxf6rXm+Sltx9k3KD/FfA9DHv6uqyuocsXbpUpv+56ULChkCiBczn0HweS0tLtWrVKs2cOVONjY0yn9mwAwlTmdQcTZ03VZ1bX9Qrx8zksOZ7UqvVj25W6IvMd6u9+SMtmDVRjEpK9CeE/BFAIF4CQW4j4lUE8kEAgaELpCqjaKZufbVGu0+cD5hMat4d2nzwbo2pm6vLrXUmLtHl0+s0ZtkP9FjplUEHiZqnEuaX3qamJi1evFh1dXWaNm2a1ZXEzI7DhkC8Bc6cOWONhzCfQ/N59I+HKC4ujnA8xHDl3f6Y6h/4vVZeZcYVZevm5z/UrY+sUHGIlfSe+Fe9+OpEzSoK86lIiOlzGgIIIGBHgRSfz9dngkizoFW/XXYsN2VCAIEegfM6UVOpJQf/XJsf+4qyYvwTgbmZe+2116wbOlOEe++9VzfeeGOEN3I9leEFAgEFTPBaX1+vZcuWaf369dYTCRPs2mbznlDDyr/Ri0XV2lgWPEi3TZkpCAIIIDAEgf6xAsHEEBC5BAHbCVy4kXlhzP16/P4pMQ8o/PU3fdV/+tOfasWKFVq9erW++tWvqrCw0H+YfxGIWMB0ZTJPIMx4iIceekjTp08fWjemiEsSJAFvp5q+t1KPfPD1uAT0QUrCIQQQQCDmAgQTMScmAwQSJODt1KGt6/XMHxZq45IJQbsvRbuE5mnFwYMH9cwzz1hJmyk4v/a1r9nvpi/aFSe9mAiY8RB79+7t+TyZrkyTJk2y6dOvj9WyaYWev2SevrVgctwC+ZjAkygCCCAQggDBRAhInIIAAkMX8HdH2bJli/UrcklJSfyn5hx68bkygQL+LnRmelfzBGL+/Pk86Upge5A1AgggEEiAYCKQCvsQQCDqAubX5cOHD1uLhr311lvWLDtm5h1b9XOPeq1JcCgC/gDUPx7CBBFDmpFpKJlzDQIIIIBAWAIEE2FxcTICCERDwCwm1tDQYM0Cde2111ozQ9m320o0akwaoQiY8RBmhWoTbJrxEHPmzLFpV6ZQasM5CCCAgDsECCbc0c7UEgHbCpgbSLMegBm0bWblMVN65uXl2ba8FCy6AuaJ1c6dO2W6wZnNjIeI+wrV0a0SqSGAAAKuEiCYcFVzU1kE7Ctg+sebGXr8N5VmsTFbztRjX0JHlcy0t1ml2rS36e522223EUQ6qgUpLAIIIPCJAMEEnwQEELCdgJlidt++fdYaAkwxa7vmiahAZjzEK6+8otraWmvcDOMhIuLkYgQQQCDhAgQTCW8CCoAAAgMJ9J4StKOjw1p9mylmB9JKzH4z/sUMlPZvo0eP9r+UGQ/j306fPq0333zTGkhtnjoxHsIvw78IIICAswUIJpzdfpQeAdcImJtW82u26RYT7qBt0ye/oKCAmaNi8GkxAd+IESNCSnnevHn60Y9+FNK5nIQAAggg4AwBgglntBOlRACBCwL+KWb9qyCbX7mDTTHrv9n90pe+ZP0ynpaWhmWUBR577DE98sgjQVOdPXu2ampqmJ0pqBIHEUAAAecJEEw4r80oMQIIXBDovaiZx+PRvffeqxtvvLHPDeuPf/xj3XLLLdYVN998s15++eU+x8GMXMC0w5/+6Z/q5MmTARP73Oc+JzNrF2uKBORhJwIIIOBogf7BRKqja0PhEUDAVQJmITPzZKKpqUmrVq3SwYMHrS43ZsVkM4jbbM8880yPiQksTFcb87SCLToCxvLdd9/VZZddFjDBMWPGyDxFIpAIyMNOBBBAIOkEUnw+n693rfpHG72P8RoBBBCwm0DvKWbNje6BAwfU1dXVp5hz587V9u3b++zjTXgCfufHH3/cmsLXLDr4wAMPqLOzsyehkSNH6vvf/76+/vWv9+zjBQIIIIBAcgn0jxV4MpFc7UttEHCdgHlaUVZWZg3Wvvrqqy8KJAyIWc/C9PNnC1/ADIQ3T35GjRolM8PWtm3btHbtWitgKCoq6pPg3/7t3xJI9BHhDQIIIJD8AjyZSP42poYIuEZg/Pjxev/99wPW19wMf+tb39LKlSsDHmdnXwEz5sE/6P2hhx4KuKCgOcdM3Xv27FkxPqWvH+8QQACBZBXo/2SCYCJZW5p6IeAyAXNj+xd/8Rf64IMPBqz58OHD9dd//df67ne/y6DsAEqmm9jevXt7xp1UVFTIdGcKNiPWF7/4RcvcjF8xT4nYEEAAAQSSW4BgIrnbl9oh4FoBs5Ca6Y4z0DZ58mRr4LY5ft1112nJkiUqLi5WXl7eQJe4Zn/vWbKmT58us0p1YWFhSPU/evSoPv3pTzPgOiQtTkIAAQScL0Aw4fw2pAYIIBBAwPzHzWxmDYorrrhCZnrSz372s1Zf/2uuucY6Zt6bX9n9g4nNgnhmM1PMmv7/bvtlvaWlRfX19daK1uvXrw+6focFxf8ggAACCLhegGDC9R8BABBAoLeAmVL2pz/9qVasWKHVq1frq1/9asi/yvdOx0mvTZewzZs366233pIZDzFnzpygXZmcVDfKigACCCAQWwGCidj6kjoCCDhUoP94ATNDlBlcnCxPK0z9du7cKf/TGDMeYsqUKQ5tLYqNAAIIIJAoAYKJRMmTLwIIOEbA3/3H3HibMQQlJSWDDkS2a+VMl66XXnrJCiJMXe666y7Gidi1sSgXAggg4AABggkHNBJFRAABewiYX/MPHz7c0yXIrL5txmQ4YXVnExC98sor1vobptxmUHWyPGWxx6eDUiCAAALuFCCYcGe7U2sEEIhQoPeMR9dee63Mqto33nij7cYa+MdDmClyTRDBeIgIG57LEUAAAQT6CBBM9OHgDQIIIBC+gLlhb2xstAZtm1mQEj3FrH88xOOPPy4T6CxevJjxEOE3K1cggAACCIQgQDARAhKnIIAAAqEI9J9i1jwJMOMS4tWdyD8ewqyxYWaiuu222xgPEUrDcQ4CCCCAwJAFCCaGTMeFCCCAwMACZorZffv2WWs2mBv7adOmxezpgBkP8dxzz2nPnj0qLy9PqlmnBhbmCAIIIICAHQQIJuzQCpQBAQSSVsA/xeyOHTusdRyidbPvHwxeXV1t2ZmF9uw4ZiNpG5aKIYAAAghYAgQTfBAQQACBOAm0t7dbsymZKWb9YxkmTZoU1qBtf1cqMx7CP00t60PEqQHJBgEEEEDgIgGCiYtI2IEAAgjEVsD/VKGurs7qmhRoilkTeHz00Uc9Yx78gYgZD2GHQd6xFSJ1BBBAAAGnCBBMOKWlKCcCCCSlgH+K2ZqaGqt+pruSmR3qO9/5jkaOHKmJEyfq+uuvt8ZfPPTQQ3Ed0J2U4FQKAQQQQCCqAgQTUeUkMQQQQGDoAmbQ9g9/+EOtXbu2J5FLLrlEGzZs0KJFi8LqDtWTAC8QQAABBBCIoQDBRAxxSRoBBBAIV8B0Z/rsZz/b5zIzKxTjIvqQ8AYBBBBAwCYC/YOJVJuUi2IggAACrhTIzs7WPffcY9X9sssu08033ywzSJsNAQQQQAABJwik+Hw+X++C9o82eh/jNQIIIIBAbATM2hFm0bmdO3dq3LhxscmEVBFAAAEEEIhQoH+sQDARISiXI4AAAtESMFPIms3M9sSGAAIIIICAHQX6BxOX2rGQlAkBBBBwo0B6erobq02dEUAAAQQcLMCYCQc3HkVHAIHkEujo6BABRXK1KbVBAAEEkl2AYCLZW5j6IYCAYwR2796tq6++2jHlpaAIIIAAAggQTPAZQAABBGwgYKaINZuZ3YkNAQQQQAABpwgQTDilpSgnAggktUBTU5NmzpyZ1HWkcggggAACySdAMJF8bUqNEEDAgQIHDhzQ1KlTHVhyiowAAggg4GYBpoZ1c+tTdwQQsI2AmWrvo48+Ulpamm3KREEQQAABBBDoL9B/alieTPQX4j0CCCCAAAIIIIAAAgiEJEAwERITJyGAAAKxFVi/fr0OHz48aCZmpWzzx4YAAggggIAdBAgm7NAKlAEBBFwvYMZLVFdXyz+rkx/kzJkzqq+vV2VlpcyjZXOO+Zs8ebLMitnnzp3zn8q/CCCAAAIIxF2AMRNxJydDBBBAILBATU2NFSCMGTNGn/70p60nEGYhu4ULF+q6667TpEmTesZUmCDj2WefVUZGhsrLywMnyF4EEEAAAQSiLNB/zATBRJSBSQ4BBBCIVMA8nTCDsUeMGBF03QkTUMyePVuNjY09QUakeXM9AggggAACwQT6BxOXBjuZYwgggAAC8RcIdeG6zMxMTZ8+Xc3NzSosLIx/QckRAQQQQMD1AoyZcP1HAAAEEHC6gHmCwYYAAggggEAiBAgmEqFOnggggECUBPbs2aPRo0dHKTWSQQABBBBAIDwBgonwvDgbAQQQsI2AGVvh8XhkujuxIYAAAgggkAgBgolEqJMnAgggEAWBhoYGzZw5MwopkQQCCCCAAAJDEyCYGJobVyGAAAIJF9i7d6/M+hRsCCCAAAIIJEqAqWETJU++CCCAQAQCZrE6M/Da5/NFkAqXIoAAAgggEJ5A/6lheTIRnh9nI4AAArYQ+M1vfqOKigpblIVCIIAAAgi4V4Bgwr1tT80RQMDBAuapREtLi4NrQNERQAABBJJBgEXrkqEVqQMCCLhOwCxsN2bMGCugyMvLC1h/0xXKLGh3/Phxpaenq6ioiJmfAkqxEwEEEEBgqAI8mRiqHNchgAACCRaYO3euqqurtX///p6SmOli6+vrtXTpUmtMxUsvvWQdM08xZs+erTVr1sgEGWwIIIAAAghEQ4AB2NFQJA0EEEAgQQImkGhsbNSKFSusEpSUlFjTxZpZnvLz82DLDFEAABkNSURBVJWWltZTMhNEPPXUU9YTiuLi4p79vEAAAQQQQCBUgf4DsAkmQpXjPAQQQCAJBMwTisrKStXW1iZBbagCAggggEC8BQgm4i1OfggggIDNBMz/EZw+fZrxEzZrF4qDAAIIOEGAYMIJrUQZEUAAgRgK9P8/ghhmRdIIIIAAAkkm0P//QxiAnWQNTHUQQACBYAKmm9Ndd90V7BSOIYAAAgggELIAwUTIVJyIAAIIOF/gwIEDuvHGG51fEWqAAAIIIGALAYIJWzQDhUAAAQTiI1BTU6OJEyfGJzNyQQABBBBIegGCiaRvYiqIAAIIfCJw5swZdXR0qLCwEBIEEEAAAQSiIkAwERVGEkEAAQTsL/Duu++qtLTU/gWlhEkm4FXXnhf0D02d8iZZzagOAghIBBN8ChBAAAGXCPz2t7/VhAkTXFJbqmkrAW+zHi9drdoT521VLAqDAAKRCxBMRG5ICggggIAjBD7zmc/IDMBmQyC+AqnKmH6fti3+3yr/h33qim/m5IYAAjEWYAXsGAOTPAIIIGAngcmTJ2vXrl0BF6wzYypMV6hf/epX+o//+A997nOfs7pFZWdn26kKlMWpAl0NqprwrPL3bNGSvOFOrQXlRsD1Aqwz4fqPAAAIIOBmgfLyci1ZskRmViez5oT5M6+XLl2qUaNGqbGxUXl5edZaFOZfc745xoaAETA3EaH8BdTK+LLufOwyvbyvjbETAYHYiYAzBXgy4cx2o9QIIIDAkAXa29tVW1ur3bt3W4GDeQIxdepU5efnKy0t7aJ0TTBx3333MQvURTLsCFfA27JJc5ZJ63cuUR4drcPl43wEbCHQ/8kEwYQtmoVCIIAAAvYV2L9/v/XEYvny5fYtJCVzhgBdnZzRTpQSgSAC/YMJfhcIgsUhBBBAAAHpyiuvVFNTExQISPKqq2G5PClFqmo41UvklBqqipTiWa6GriATwKZ7lF9wQs3t3b2u5SUCCDhZgGDCya1H2RFAAIE4CJw6dcrqDhWHrMgi2QVSRyunUDrSdopxE8ne1tTPNQIEE65paiqKAAIIDE3g17/+ta655pqhXcxVCPQRSFd2/jjVv/xztQZ5gNHnEt4ggICtBQgmbN08FA4BBBBIvICZ7emGG25IfEEoQdwFzGxfMdmOtqq9m2giJrYkikCcBQgm4gxOdggggICTBMzMTx0dHXRzclKjRVhW0+ZbtmyRWZOksrJSZv2R6G3DNDYnV1mdrWo7yWrY0XMlJQQSJ3Bp4rImZwQQQAABuwu88847Wrhwod2LSfkiFDABRENDg7XmiEmqrKzMes2ChRHCcjkCLhAgmHBBI1NFBBBAYKgCBw8e1LRp04Z6OdfZWMA8cTDt+8wzz1hPn0zQuHbt2kGeQqUqPTtXBaqPsGbHP5nRiZWwI3TkcgQSL0A3p8S3ASVAAAEEbCtw9uxZjRkzxrblo2DhCZgAor6+3lrVfPbs2dYK6KtWrbKm/jWrnZtVzwfbUnO/rHnFHdr6wk90zBr30KWWmif16NpDg13a63gHMzr10uAlAk4WIJhwcutRdgQQQCDGAmbgtbn5ZHOuwLlz52QWHjTjH0aNGmU9jVi8eHFPAFFYWBhe5VLzdPv6f9IDWqerLr9EKSlz9fzvivXIP84NLx3ORgCBpBBgBeykaEYqgQACCMRGwPySbX7BbmxsVFpaWp9M/N1kTFeZ2tpa/fKXv1RFRYVKSko0adKki87vczFvYipgAojDhw9b7bZixQqtXr3a6q6W+HYxi96t1ISbNqvg+QbtXDJB/KoZ048CiSMQdYH+K2AzZiLqxCSIAAIIJI9AZmamHnroIY0YMULr16+3usGcPHlSe/fu1XPPPddzk3rPPffInGt+Aa+rq7P+TP97tvgKHDlyRPv27bNmY7r22ms1d+5cnT592mqb+JZksNw6dbS5Q92aoIzBTuU4AgjYWoAnE7ZuHgqHAAII2EPA/NJtAgjzFGLChAkaP368gnWPMdOK7tq1y4Y3sfbwjGYpAgUQRUVFNrX/WC2bFir/zh3KqnxTx56YQTARzQ8DaSEQBwGeTMQBmSwQQACBZBMwXZyKi4utv1DqZgbzvvbaa0wrGwrWEM5hKtchoHEJAgjERIBuTjFhJVEEEEDA3QJjx461Zgpyt0J0ax8ogNiwYYNYCyK6zqSGAALhCRBMhOfF2QgggAACIQiYcRUejyeEMzklmIB/kPuOHTv01ltvWU96zFSuwbqYBUsv8ce61d58PPHFoAQIIBA1AYKJqFGSEAIIIICAX6CmpsZaAM3/nn9DFwgUQNx3330ODiBCrztnIoCA8wQIJpzXZpQYAQQQsLWA6Y7T0dER0gJotq5IHAsXaCpXsxZE4qdyjRVClgryPUqPVfKkiwACcRMgmIgbNRkhgAAC7hB45513GHgdQlMHCiCmTZumjz76KHnX6PCeUtuRjhB0OAUBBJwiQDDhlJainAgggIBDBHbv3q358+c7pLTxL2agqVztuRZE/G3IEQEEnCdAMOG8NqPECCCAgK0Fqqur9e1vf9vWZYx34QIFEO5eh8OjwpzRrH4d7w8i+SEQAwGCiRigkiQCCCCAAAKBpnI1A9NdPZVrd4eaj3ZKYqYvviEIJIsAwUSytCT1QAABBGwisH79emu1bLPIXbCtpaXFOpyXlxfsNEcdCxRAsBZEoCYcr/xshl8HkmEfAk4TIJhwWotRXgQQQMDmAiaIqKys1NVXX93nV3j/lKcHDx7UihUrVFJSojFjxuiDDz6wBmzPmTPHkQOP/fVKnrUgbP4Bo3gIIGArAYIJWzUHhUEAAQScL2CeNCxcuFDl5eVWsPD5z39e77//vp577jmtXr1a/WcsMr/mb9myxZpO1lzjhC1QAMFaEGG0XFaucsYOC+MCTkUAAbsKpPh8Pl/vwqWkpKjfrt6HeY0AAggggEDIAmbg8YcffmgFFcG6M5mb89mzZ6uxsdG2TycGmso1edeCCLmZQz+xq0FVE27SWj2sN489phkZqaFfy5kIIGALgf6xAk8mbNEsFAIBBBBIToHCwsKQKpaZmanS0lIdPnxYU6ZMCemaeJw0UACR1GtBxAO2IFfZ6QQS8aAmDwRiLUAwEWth0kcAAQQQcJxAoKlcWQsiCs2Y7lF+QVYUEiIJBBCwiwDBhF1agnIggAACLhdoampK6MrZgQIId68F4fIPJNVHAIGQBAgmQmLiJAQQQACBWAqYQdgdHR19Zn+KZX7+tANN5er6tSD8OLH4N3W0cgo90pFYJE6aCCCQCAGCiUSokycCCCCAQB+Bd955J25PJQIFEKwF0ac5YvgmXdn54wkmYihM0gjEW4BgIt7i5IcAAgggcJGAWaPBTK0aqy3QVK6rVq1SqAPEY1Uu96U7TGNzcsWoCfe1PDVOXgGmhk3etqVmCCCAgGMEzFSD0Z4hyczEtHfvXplAxaxxYVbmnjp1KgFEgj8V3pZNmjO9VVVMDZvgliB7BIYm0H9qWOZlG5ojVyGAAAIIREmgpaVFd911V1TWlzABxP79+7VmzRqNGDFCZrXtxYsXW4GKWRCPJxFRarQIkkkdm6NCtart5PkIUrn40t8fWqfclBSZG53ef7nrDun3F5/OHgQQiJIA3ZyiBEkyCCCAAAJDEzA3/R988EFIF5tgYcWKFdaK2gUFBXr44YetIMQEEGbBO3OsoqJCJSUlUX/SEVIBOWlwAWt62BNqbu+W8oYPfn6IZ1x6/YNq9T0Y4tmchgAC0RIgmIiWJOkggAACCAxJIDs721oh20zNGuzJgXmCsXLlSqvbksmotrZWv/zlL2XWf7j22ms1d+5c67VZAI/NxgKpOZo6L0cvt52SV6NFFwkbtxVFQyAEAYKJEJA4BQEEEEAgtgKmK9LTTz9tdUnyr4BtBk2/++67PU8cTFeo9957r09Bzp49K9aC6EPigDfDlTv1Jl32fIe6NUEZDigxRUQAgYEF+EFgYBuOIIAAAgjEScAEECagqKur0+TJk62/2bNnW4HEtGnTrCcOGzdu1Lx58/qU6MCBA3rppZdkAg825wik5n5ZZf+2Rwe7vCEU2qvuYy9okafvWAjGRYRAxykIxEGAJxNxQCYLBBBAAIHBBUxAYf78gUGg7krLli2zEjIDq6dPn26Njfjnf/5njRo1ypqtaf78+Qp03eC5c0ZcBUxXp7L3dPc/HtTkBycrPVjm3hZtr27XokOn9c0X79H2Sc/oiRnnVLPoq/rBtB3auWQCXaWC+XEMgRgL8GQixsAkjwACCCAQnoAJBgYKCNLS0lRZWant27fr3nvv1bhx42RmaTLjJsxmggqzAJ0/IAkvZ86On8Bw5d12pyY/+R09e+hskGy96tpTq9a/ulszsoZJStOYK4ZL3g919qQ0duSnCCSC6HEIgXgIEEzEQ5k8EEAAAQRiKmCCD39QkZGRIdNFygQVZrVrNpsKZEzVNzfk6MnlNWoZsLdTqjJmPKQ1M0ZL+j/696NS5uWXWsHEmff+RGNHptm0chQLAfcIEEy4p62pKQIIIJD0AiaoWLhwoTXWwuPxqKyszHqSYWaCYrObgFcfnv1PdYZarN//p47vT9NIE0xY2+WfPKUI9XrOQwCBmAgQTMSElUQRQAABBBIpYLpDmUDCrD1xww036I477iCoSGSDBMjbe+KnemLlR6peU6a8EO5GvMff0hvK1ZVj/MFEgETZhQACcRcI4esb9zKRIQIIIIAAAlERIKiICmMMEvlYra+/qvbH1umB60cOnr7331X7xFOqnzJeHhNLpH5KmV/4jX7ys3fUdaJOf/fCMQ3YU2rw1DkDAQQiECCYiACPSxFAAAEEnCHQO6gwq2ObQdzmz6yczZYAAW+b9tV8QVW35YU0gPr3v9qhyk3SkpLr9RlT3NTxmlO1QKr4oiYsb9fXiseHlE4CakqWCCS9QIrP5/P1rqWZt7nfrt6HeY0AAggggEBSCJhAorq62qpLRUWFNS1tUlTMAZXwtmzSLc/n6KUnZrBonQPaiyIi0Fugf6xAMNFbh9cIIIAAAq4TIKiId5N/rJZNd2qZHmGNiHjTkx8CURAgmIgCIkkggAACCCSfAEFFnNrUe0yb5typ5qo6PWFN+RqnfMkGAQSiItA/mGDMRFRYSQQBBBBAwOkCZvXt2tparV27VnV1dSotLVVNTY3OnTvn9KrZq/zdHWo+Ok752UHXvbZXmSkNAggMKEAwMSANBxBAAAEE3CiQl5dnBRQmqDhw4ICmTZtGUBHFD4L3ZJuOKFc5Y82K1mwIIOB0AYIJp7cg5UcAAQQQiImAP6jYtm0bQUXUhL3qbm/V0YJcZadzCxI1VhJCIIECfJMTiE/WCCCAAAL2F+gdVBw7downFRE12XmdbGsNfdXriPLiYgQQiIcAwUQ8lMkDAQQQQMDxAiaoWL58uXbt2qWOjg6NGDFCGzZs0JkzZxxft/hVoFvtzcfjlx05IYBAzAUIJmJOTAYIIIAAAskkkJmZqfLycp0+fdqq1qhRowgqQm1g7ym1HekI9WzOQwABBwgQTDigkSgiAggggID9BAgq7NcmlAgBBOIvQDARf3NyRAABBBBIIoHeQUVGRoZmz55tPaloaWlJolpGqSrWtLCdUUqMZBBAwA4CBBN2aAXKgAACCCDgeAETVCxcuFCNjY3yeDy64447VFlZKYKKAE17tFXt3d4AB9iFAAJOEyCYcFqLUV4EEEAAAVsLpKWlqayszAoqbrjhBoIKW7cWhUMAgUgFCCYiFeR6BBBAAAEEAggQVARAYRcCCCSdAMFE0jUpFUIAAQQQsJNA76CipKTE6vq0dOlS7d+/307FjG9ZOlvVdvJ8fPMkNwQQiIkAwURMWEkUAQQQQACBvgImqJgyZYpqa2u1ePFiVVdXq7S01N1BRV8i3iGAgAMFCCYc2GgUGQEEEEDA2QL+oKKiosJdQUW6R/kFWc5uPEqPAAJ9BAgm+nDwBgEEEEAAgfgJ9A4qNm/e7KInFcfV3N4dP2hyQgCBmAkQTMSMloQRQAABBBAITcAEFRs3btTatWtVV1enyZMnq6amRufOnQstAc5CAAEEEiRAMJEgeLJFAAEEEECgv0BeXp4VUGzbtk0HDhzQtGnTCCr6I/EeAQRsJUAwYavmoDAIIIAAAghISRtUpI5WTqGHJkYAgSQSIJhIosakKggggAACySXQO6jo6OjoeVJx5swZh1e0Q0faTok1sB3ejBQfAUkEE3wMEEAAAQQQsLmACSrKy8u1a9cumaBi1KhR2rBhg5wfVNgcnuIhgMCgAgQTgxJxAgIIIIAAAvYQyMzMtIKK06dPWwVyXlCRruz88fbApBQIIBAVAYKJqDCSCAIIIIAAAvETcH5QET8rckIAgdgKEEzE1pfUEUAAAQQQiJlA76DC4/Fo9uzZVvenlpaWmOVJwggggEBvAYKJ3hq8RgABBBBAwIECJqgoKytTY2OjTFBxxx13qLKyUvYNKjwqzBnNwE0HftYoMgL9BQgm+ovwHgEEEEAAAYcKpKWl9QQVN9xwQ/yCiq4GVXk8mrXpGDM0OfSzQ7ERGKoAwcRQ5bgOAQQQQAABmwokLKgI2WO88rPTQz6bExFAwL4CBBP2bRtKhgACCCCAQEQC/qCiqalJJSUlVtenpUuXav/+/RGly8UIIICAX4Bgwi/BvwgggAACCCSxwJQpU1RbW6vFixerurpapaWlQwwqzqvzUI3WLSpQSkqKUjyLtG7nYZ0Mxy4rVzljh4VzBecigIBNBQgmbNowFAsBBBBAAIFYCPiDioqKiiEEFV51H3pa84t+oA9Kduh3Pp98LQ9r/OE3tKUzjNIW5Co7nVuQMMQ4FQHbCvBNtm3TUDAEEEAAAQRiJ9A7qNi8eXPPk4pz584FyfSMmra/qObKKq0omyBr1EP6BJWtqFJlVpDLOIQAAkkrQDCRtE1LxRBAAAEEEBhcwAQVGzdu1Nq1a1VXV6dp06apvr4+8IVdv9brWztUkO/5JJDwn5XuUX7BCP+7IP92q735uLIKczSWO5AgThxCwDkClzqnqJQUAQQQQAABBGIlkJeXZwUUZm2Kt99+O2A23pNtOhJOd6b+qXhPqe3In2hB1URl9D/GewQQcKQAwYQjm41CI4AAAgggEBsBE1SYv0Bb6tgcFWZJRwIdDGVfd4eaj45jWthQrDgHAYcI8JDRIQ1FMRFAAAEEEEi4QMZEzVrg0dHmDnX3LowVJHzUe0/A19aTDTGTU0AcdiLgUAGCCYc2HMVGAAEEEEAg/gKjNf2byzVn6/1atuntTwKK7mOqWf2E1g7a/eljte7bpaMLZqoog9uP+LcdOSIQGwG+zbFxJVUEEEAAAQSSUiB1XKm+t2edChr/UpebdSYuv1+/+LMlqi4eZAC2t037Xj6hBbMYL5GUHwwq5VqBFJ/P5+tde7MATb9dvQ/zGgEEEEAAAQQQCFPArE/xPd188wd65NhjmsGTiTD9OB0B+wj0jxUYgG2ftqEkCCCAAAIIJKWAt/NNrXnwaQ177DVNJ5BIyjamUu4VIJhwb9tTcwQQQAABBOIg8LFad27U3+s+Hbw9T/SvjgM5WSAQRwGCiThikxUCCCCAAAKuFBj5Fb36g3m6Pp1QwpXtT6WTWoAxE0ndvFQOAQQQQAABBBBAAIHoCfQfM8FPBNGzJSUEEEAAAQQQQAABBFwlQDDhquamsggggAACCCCAAAIIRE+AYCJ6lqSEAAIIIIAAAggggICrBAgmXNXcVBYBBBBAAAEEEEAAgegJEExEz5KUEEAAAQQQQAABBBBwlQDBhKuam8oigAACCCCAAAIIIBA9AYKJ6FmSEgIIIIAAAggggAACrhIgmHBVc1NZBBBAAAEEEEAAAQSiJ0AwET1LUkIAAQQQQAABBBBAwFUCBBOuam4qiwACCCCAAAIIIIBA9AQIJqJnSUoIIIAAAggggAACCLhKgGDCVc1NZRFAAAEEEEAAAQQQiJ4AwUT0LEkJAQQQQAABBBBAAAFXCRBMuKq5qSwCCCCAAAIIIIAAAtETIJiIniUpIYAAAggggAACCCDgKgGCCVc1N5VFAAEEEEAAAQQQQCB6AgQT0bMkJQQQQAABBBBAAAEEXCVAMOGq5qayCCCAAAIIIIAAAghET4BgInqWpIQAAggggAACCCCAgKsECCZc1dxUFgEEEEAAAQQQQACB6AkQTETPkpQQQAABBBBAAAEEEHCVAMGEq5qbyiKAAAIIIIAAAgggED0BgonoWZISAggggAACCCCAAAKuEiCYcFVzU1kEEEAAAQQQQAABBKInQDARPUtSQgABBBBAAAEEEEDAVQIEE65qbiqLAAIIIIAAAggggED0BAgmomdJSggggAACCCCAAAIIuEogxefz+fw1TklJ8b/kXwQQQAABBBBAAAEEEEAgoIA/hLi091H/zt77eI0AAggggAACCCCAAAIIBBKgm1MgFfYhgAACCCCAAAIIIIDAoAIEE4MScQICCCCAAAIIIIAAAggEEiCYCKTCPgQQQAABBBBAAAEEEBhUgGBiUCJOQAABBBBAAAEEEEAAgUAC/x94EH8I9r3ZzAAAAABJRU5ErkJggg=="></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the quark structures of a meson and a baryon.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain which interaction is responsible for this decay.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw arrow heads on the lines representing <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar u}">
<mrow>
<mrow>
<mover>
<mi>u</mi>
<mo stretchy="false">¯</mo>
</mover>
</mrow>
</mrow>
</math></span> and d in the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\pi ^ - }">
<mrow>
<msup>
<mi>π</mi>
<mo>−</mo>
</msup>
</mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the exchange particle in this decay.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline <strong>one</strong> benefit of international cooperation in the construction or use of high-energy particle accelerators.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>Meson:</em> quark-antiquark pair<br><em>Baryon:</em> 3 quarks</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>Alternative 1</strong></em></p>
<p>strange quark changes «flavour» to an up quark</p>
<p>changes in quarks/strangeness happen only by the weak interaction</p>
<p> </p>
<p><em><strong>Alternative 2</strong></em></p>
<p>Strangeness is not conserved in this decay «because the strange quark changes to an up quark»</p>
<p>Strangeness is not conserved during the weak interaction</p>
<p> </p>
<p><em>Do not allow a bald answer of weak interaction.</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>arrows drawn in the direction shown</p>
<p><img src="data:image/png;base64,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"></p>
<p> </p>
<p><em>Both needed for <strong>[1]</strong> mark.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>W <sup>−</sup></em></p>
<p> </p>
<p><em>Do not allow W or W<sup>+</sup>.</em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>it lowers the cost to individual nations, as the costs are shared</p>
<p>international co-operation leads to international understanding <em><strong>OR</strong> </em>historical example of co-operation <strong><em>OR</em> </strong>co-operation always allows science to proceed</p>
<p>large quantities of data are produced that are more than one institution/research group can handle co-operation allows effective analysis</p>
<p> </p>
<p><em>Any one.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A heater in an electric shower has a power of 8.5 kW when connected to a 240 V electrical supply. It is connected to the electrical supply by a copper cable.</p>
<p>The following data are available:</p>
<p style="padding-left: 120px;">Length of cable = 10 m<br>Cross-sectional area of cable = 6.0 mm<sup>2</sup><br>Resistivity of copper = 1.7 × 10<sup>–8</sup> Ω m</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the current in the copper cable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the resistance of the cable.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, in terms of electrons, what happens to the resistance of the cable as the temperature of the cable increases.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The heater changes the temperature of the water by 35 K. The specific heat capacity of water is 4200 J kg<sup>–1</sup> K<sup>–1</sup>.</p>
<p>Determine the rate at which water flows through the shower. State an appropriate unit for your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>I</em> «=<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{8.5 \times {{10}^3}}}{{240}}">
<mfrac>
<mrow>
<mn>8.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>240</mn>
</mrow>
</mfrac>
</math></span>» =35«A»</p>
<p> </p>
<p> </p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>R </em>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.7 \times {{10}^{ - 8}} \times 10}}{{6.0 \times {{10}^{ - 6}}}}">
<mfrac>
<mrow>
<mn>1.7</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>8</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>10</mn>
</mrow>
<mrow>
<mn>6.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>= 0.028 «Ω»</p>
<p> </p>
<p><em>Allow missed powers of 10 for MP1.</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«as temperature increases» there is greater vibration of the metal atoms/lattice/lattice ions</p>
<p><em><strong>OR</strong></em></p>
<p>increased collisions of electrons</p>
<p> </p>
<p>drift velocity decreases «so current decreases»</p>
<p>«as V constant so» <em>R</em> increases</p>
<p> </p>
<p><em>Award <strong>[0]</strong> for suggestions that the speed of electrons increases so resistance decreases.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that power = flow rate × cΔ<em>T</em></p>
<p>flow rate «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{{\text{power}}}}{{c\Delta T}}">
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<mtext>power</mtext>
</mrow>
</mrow>
<mrow>
<mi>c</mi>
<mi mathvariant="normal">Δ</mi>
<mi>T</mi>
</mrow>
</mfrac>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{8.5 \times {{10}^3}}}{{4200 \times 35}}">
<mo>=</mo>
<mfrac>
<mrow>
<mn>8.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4200</mn>
<mo>×</mo>
<mn>35</mn>
</mrow>
</mfrac>
</math></span></p>
<p>= 0.058 «kg s<sup>–1</sup>»</p>
<p>kg s<sup>−1</sup> / g s<sup>−1</sup> / l s<sup>−1</sup> / ml s<sup>−1</sup> / m<sup>3</sup> s<sup>−1</sup></p>
<p> </p>
<p><em>Allow MP4 if a bald flow rate unit is stated. Do not allow imperial units.</em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph shows how current <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math> varies with potential difference <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> across a component X.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" width="532" height="357"></p>
</div>
<div class="specification">
<p>Component X and a cell of negligible internal resistance are placed in a circuit.</p>
<p>A variable resistor R is connected in series with component X. The ammeter reads <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi>mA</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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" width="187" height="157"></p>
</div>
<div class="specification">
<p>Component X and the cell are now placed in a potential divider circuit.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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" width="241" height="131"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why component X is considered non-ohmic.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the resistance of the variable resistor.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the power dissipated in the circuit.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the range of current that the ammeter can measure as the slider S of the potential divider is moved from Q to P.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe, by reference to your answer for (c)(i), the advantage of the potential divider arrangement over the arrangement in (b).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">current is not «directly» proportional to the potential difference<br></span><span class="fontstyle2"><em><strong>OR</strong></em><br></span><span class="fontstyle0">resistance of X is not constant<br></span><span class="fontstyle2"><em><strong>OR</strong></em><br></span><span class="fontstyle0">resistance of X changes «with current/voltage» </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><span class="fontstyle0">voltage across X<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">V</mi><mo>»</mo></math> ✓</span></p>
<p><span class="fontstyle0">voltage across R<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>-</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>»</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>7</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">V</mi><mo>»</mo></math> ✓</span></p>
<p><span class="fontstyle0">resistance of variable resistor <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>7</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>85</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">Ω</mi><mo>»</mo></math> ✓</span></p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>overall resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>0</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>200</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">Ω</mi><mo>»</mo></math> ✓</p>
<p>resistance of X <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>3</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow></mfrac><mo>»</mo><mo>=</mo><mn>115</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">Ω</mi><mo>»</mo></math> ✓</p>
<p>resistance of variable resistor <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mn>200</mn><mo>-</mo><mn>115</mn><mo>»</mo><mo>=</mo><mn>85</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">Ω</mi><mo>»</mo></math> ✓</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>power <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>«</mo><mo>=</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>020</mn><mo>»</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>080</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">W</mi><mo>»</mo></math> <span class="fontstyle0">✓</span></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mi>mA</mi></math> </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">allows zero current through component X / potential divider arrangement </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">provides greater range </span><span class="fontstyle3">«</span><span class="fontstyle0">of current through component X</span><span class="fontstyle3">» </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>Electrical resistors can be made by forming a thin film of carbon on a layer of an insulating material.</p>
</div>
<div class="specification">
<p>A carbon film resistor is made from a film of width 8.0 mm and of thickness 2.0 μm. The diagram shows the direction of charge flow through the resistor.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The resistance of the carbon film is 82 Ω. The resistivity of carbon is 4.1 x 10<sup>–5</sup> Ω m. Calculate the length <em>l</em> of the film.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why knowledge of quantities such as resistivity is useful to scientists.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The current direction is now changed so that charge flows vertically through the film.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Deduce, without calculation, the change in the resistance.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a circuit diagram to show how you could measure the resistance of the carbon-film resistor using a potential divider arrangement to limit the potential difference across the resistor.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«<em>l</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{RA}}{\rho } = \frac{{82 \times 8 \times {{10}^{ - 3}} \times 2 \times {{10}^{ - 6}}}}{{4.1 \times {{10}^{ - 5}}}}">
<mfrac>
<mrow>
<mi>R</mi>
<mi>A</mi>
</mrow>
<mi>ρ</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>82</mn>
<mo>×</mo>
<mn>8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>4.1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>»</p>
<p>0.032 «m»</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>power = 1500 × 8 × 10<sup>–3</sup> × 0.032 «= 0.384»</p>
<p>«current ≤ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {\frac{{{\text{power}}}}{{{\text{resistance}}}}} = \sqrt {\frac{{0.384}}{{82}}} ">
<msqrt>
<mfrac>
<mrow>
<mrow>
<mtext>power</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>resistance</mtext>
</mrow>
</mrow>
</mfrac>
</msqrt>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<mn>0.384</mn>
</mrow>
<mrow>
<mn>82</mn>
</mrow>
</mfrac>
</msqrt>
</math></span>»</p>
<p>0.068 «A»</p>
<p> </p>
<p><em>Be aware of ECF from (a)(i)</em></p>
<p><em>Award <strong>[1]</strong> for 4.3 «A» where candidate has not calculated area</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>quantities such as resistivity depend on the material</p>
<p><em><strong>OR</strong></em></p>
<p>they allow the selection of the correct material</p>
<p><em><strong>OR</strong></em></p>
<p>they allow scientists to compare properties of materials</p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>as area is larger <strong>and</strong> length is smaller</p>
<p>resistance is «very much» smaller</p>
<p><em>Award <strong>[1 max]</strong> for answers that involve a calculation</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>complete functional circuit with ammeter in series with resistor and voltmeter across it</p>
<p>potential divider arrangement correct</p>
<p><em>eg:</em></p>
<p><em><img src="data:image/png;base64,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"></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A mass of 1.0 kg of water is brought to its boiling point of 100 °C using an electric heater of power 1.6 kW.</p>
</div>
<div class="specification">
<p>A mass of 0.86 kg of water remains after it has boiled for 200 s.</p>
</div>
<div class="specification">
<p>The electric heater has two identical resistors connected in parallel.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The circuit transfers 1.6 kW when switch A only is closed. The external voltage is 220 V.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The molar mass of water is 18 g mol<sup>−1</sup>. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one</strong> assumption of the kinetic model of an ideal gas.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the specific latent heat of vaporization of water. State an appropriate unit for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the temperature of water remains at 100 °C during this time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The heater is removed and a mass of 0.30 kg of pasta at −10 °C is added to the boiling water.</p>
<p>Determine the equilibrium temperature of the pasta and water after the pasta is added. Other heat transfers are negligible.</p>
<p style="padding-left:180px;">Specific heat capacity of pasta = 1.8 kJ kg<sup>−1</sup> K<sup>−1</sup><br>Specific heat capacity of water = 4.2 kJ kg<sup>−1</sup> K<sup>−1</sup></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that each resistor has a resistance of about 30 Ω.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the power transferred by the heater when both switches are closed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>E</em><sub>k</sub> = « <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>(</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>)</mo><mo>(</mo><mn>373</mn><mo>)</mo></math>» = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>21</mn></mrow></msup></math> «J» <strong>✓</strong></p>
<p><em>v = </em>«<em><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>3</mn><mo>×</mo><mn>1</mn><mo>.</mo><mn>38</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>23</mn></mrow></msup><mo>×</mo><mn>6</mn><mo>.</mo><mn>02</mn><mo>×</mo><msup><mn>10</mn><mn>23</mn></msup><mo>×</mo><mn>373</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>018</mn></mrow></mfrac></msqrt></math></em>»<em> = </em>720 «m s<sup>−1</sup>» <strong>✓</strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>particles can be considered points «without dimensions» <strong>✓</strong></p>
<p>no intermolecular forces/no forces between particles «except during collisions»<strong>✓</strong></p>
<p>the volume of a particle is negligible compared to volume of gas <strong>✓</strong></p>
<p>collisions between particles are elastic <strong>✓</strong></p>
<p>time between particle collisions are greater than time of collision <strong>✓</strong></p>
<p>no intermolecular PE/no PE between particles <strong>✓</strong></p>
<p> </p>
<p><em>Accept reference to atoms/molecules for “particle”</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<em>mL = P</em> t» so «<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfrac><mrow><mn>1600</mn><mo>×</mo><mn>200</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>14</mn></mrow></mfrac></math>» = 2.3 x 10<sup>6</sup> «J kg<sup>-1</sup>» <strong>✓</strong></p>
<p>J kg<sup>−1 </sup><strong>✓</strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«all» of the energy added is used to increase the «intermolecular» potential energy of the particles/break «intermolecular» bonds/<strong>OWTTE</strong> <strong>✓</strong></p>
<p><em>Accept reference to atoms/molecules for “particle”</em> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of mcΔT <strong>✓</strong></p>
<p>0.86 × 4200 × (100 – <em>T</em>) = 0.3 × 1800 × (<em>T</em> +10) <strong>✓</strong></p>
<p><em>T</em><sub>eq</sub> = 85.69«°C» ≅ 86«°C» <strong>✓</strong></p>
<p><em>Accept T<sub>eq</sub> in Kelvin (359 K).</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfrac><msup><mi>v</mi><mn>2</mn></msup><mi>R</mi></mfrac><mo> </mo><mi>so</mi><mo> </mo><mfrac><msup><mn>220</mn><mn>2</mn></msup><mn>1600</mn></mfrac><mo> </mo><mi>so</mi><mo> </mo><mi>R</mi><mo>=</mo><mn>30</mn><mo>.</mo><mn>25</mn></math> «Ω» <strong>✓</strong></p>
<p><em>Must see either the substituted values <strong>OR</strong> a value for R to at least three s.f.</em></p>
<p> </p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of parallel resistors addition so <em>R</em><sub>eq</sub> = 15 «Ω» <strong>✓</strong></p>
<p><em>P</em> = 3200 «W» <strong>✓</strong></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>An electron moves in circular motion in a uniform magnetic field.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_18.05.11.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/05"></p>
<p>The velocity of the electron at point P is 6.8 × 10<sup>5</sup> m s<sup>–1</sup> in the direction shown.</p>
<p>The magnitude of the magnetic field is 8.5 T.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the direction of the magnetic field.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, in N, the magnitude of the magnetic force acting on the electron.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the electron moves at constant speed.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the electron moves on a circular path.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>out of the page plane / ⊙</p>
<p> </p>
<p><em>Do not accept just “up” or “outwards”.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>1.60 × 10<sup>–19</sup> × 6.8 × 10<sup>5</sup> × 8.5 = 9.2 × 10<sup>–13</sup> <strong>«</strong>N<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the magnetic force does not do work on the electron hence does not change the electron’s kinetic energy</p>
<p><strong><em>OR</em></strong></p>
<p>the magnetic force/acceleration is at right angles to velocity</p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the velocity of the electron is at right angles to the magnetic field</p>
<p>(therefore) there is a centripetal acceleration / force acting on the charge</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>An ohmic conductor is connected to an ideal ammeter and to a power supply of output voltage V.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-10_om_17.57.33.png" alt="M18/4/PHYSI/SP2/ENG/TZ1/04"></p>
<p>The following data are available for the conductor:</p>
<p> density of free electrons = 8.5 × 10<sup>22</sup> cm<sup>−3</sup></p>
<p> resistivity ρ = 1.7 × 10<sup>−8</sup> Ωm</p>
<p> dimensions w × h × l = 0.020 cm × 0.020 cm × 10 cm.</p>
<p> </p>
<p>The ammeter reading is 2.0 A.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the resistance of the conductor.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the drift speed <em>v </em>of the electrons in the conductor in cm s<sup>–1</sup>. State your answer to an appropriate number of significant figures.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>1.7 × 10<sup>–8</sup> × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.10}}{{{{(0.02 \times {{10}^{ - 2}})}^2}}}">
<mfrac>
<mrow>
<mn>0.10</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.02</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>0.043 <strong>«</strong>Ω<strong>»</strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>v</em> <strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{I}{{neA}}">
<mfrac>
<mi>I</mi>
<mrow>
<mi>n</mi>
<mi>e</mi>
<mi>A</mi>
</mrow>
</mfrac>
</math></span><strong>»</strong> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{{8.5 \times {{10}^{22}} \times 1.60 \times {{10}^{ - 19}} \times {{0.02}^2}}}">
<mfrac>
<mn>2</mn>
<mrow>
<mn>8.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>22</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>1.60</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>0.02</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>0.368 <strong>«</strong>cms<sup>–1</sup><strong>»</strong></p>
<p>0.37 <strong>«</strong>cms<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[2 max] </em></strong><em>if answer is not expressed to 2 sf.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows a potential divider circuit used to measure the emf <em>E </em>of a cell X. Both cells have negligible internal resistance.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_13.01.10.png" alt="M18/4/PHYSI/SP2/ENG/TZ2/04"></p>
</div>
<div class="specification">
<p>AB is a wire of uniform cross-section and length 1.0 m. The resistance of wire AB is 80 Ω. When the length of AC is 0.35 m the current in cell X is zero.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by the emf of a cell.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the resistance of the wire AC is 28 Ω.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine <em>E</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the work done per unit charge</p>
<p>in moving charge from one terminal of a cell to the other / all the way round the circuit</p>
<p> </p>
<p><em>Award </em><strong><em>[1] </em></strong><em>for “energy per unit charge provided by the cell”/“power per unit current”</em></p>
<p><em>Award </em><strong><em>[1] </em></strong><em>for “potential difference across the terminals of the cell when no current is flowing” </em></p>
<p><em>Do not accept “potential difference across terminals of cell”</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the resistance is proportional to length / see 0.35 <strong><em>AND </em></strong>1«.00»</p>
<p>so it equals 0.35 × 80</p>
<p><strong>«</strong>= 28 Ω<strong>»</strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>current leaving 12 V cell is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12}}{{80}}">
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mrow>
<mn>80</mn>
</mrow>
</mfrac>
</math></span> = 0.15 <strong>«</strong>A<strong>»</strong></p>
<p><strong><em>OR</em></strong></p>
<p><em>E</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{12}}{{80}}">
<mfrac>
<mrow>
<mn>12</mn>
</mrow>
<mrow>
<mn>80</mn>
</mrow>
</mfrac>
</math></span> × 28</p>
<p><em>E</em> = <strong>«</strong>0.15 × 28 =<strong>»</strong> 4.2 <strong>«</strong>V<strong>»</strong></p>
<p> </p>
<p><em>Award </em><strong><em>[2] </em></strong><em>for a bald correct answer</em></p>
<p><em>Allow a 1sf answer of 4 if it comes from a calculation.</em></p>
<p><em>Do not allow a bald answer of 4 </em><strong>«</strong><em>V</em><strong>»</strong></p>
<p><em>Allow ECF from incorrect current</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A proton moves along a circular path in a region of a uniform magnetic field. The magnetic field is directed into the plane of the page.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label with arrows on the diagram the magnetic force <em>F</em> on the proton. </span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label with arrows on the velocity vector <em>v</em> of the proton.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The speed of the proton is 2.16 × 10<sup>6</sup> m s<sup>-1</sup> and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><em>F</em> towards centre ✔</span></p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;"><em>v</em> tangent to circle and in the direction shown in the diagram ✔</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVsAAAEaCAYAAAC/y/QkAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAFXwSURBVHhe7d0LXE/3/wfw1/KVdNFdJUlas6RUEutPs9aaXzMzDHM3DMtcxhbDMAxzWc39OncKoSU0QpJcKiRJay1fSbpf1Fe+Ov/zOd9Pt7G5pb6d7+fpYZ3P+/tN+346530+53M+5/N5g+OBYRiGea3U6FeGYRjmNWLJlmEYpg6wZMswDFMHWJ8t02AkJqZCTw/Q1jeCjoYOjQIZ+RnIz5BBz0gCM2MLGmUY5cJatkyDUFBQgHbt2qBFizZY8vNSGgUuR0ajhX4L4bUdvwXQKMMoH5ZsmQZBV1cXTm3the3UxBThKzHum3HCVzsne0z65mthm2GUEUu2TIPRuUc34WtySrLwdf3mzYi5dFXY3uK3Dk0kTYRthlFGLNkyDYalVSvha3Z2tvB117ZtwteZM2fC1d1N2GYYZcWSLdNgWOopkm1auhSRkZE4e/YsOr3TGb6zfIU4wygzNhqBaTBSklPx5ltthG0rKyukpqbiwoVLcHV1EWIMo8xYy5ZpMKxtrOBkbytsk0Q7ZcoUlmiZBoO1bJkGJTAwED6jRkLbzBRXLsRCV1+XvsIwyo0lW6ZBkfF/M/KzYKahAw0NDUWQYRoAlmwZhmHqAOuzZUSltEiOlStXokhWRCMMoxxYsmVE5c69ZEycOBFtdJpj7o8L8OBBKX2FYeoX60ZgRCU5NRVvtVEMDyO8vDxw/PhJWmKY+sNatoyoyMtK6JZCWFg43Lt3R9iBYJSXl9Mow9Q9lmwZUUmXptOtKmfPnMGH/T6Bi7MjMtIzaJRh6hZLtozo6enpoU//PvBbtQZm5mY0yjB1iyVbRlTKyshI3JouxsbiQMABuHftSiMMU/dYsmVEJSsrT/gq0dbAsCFD0O3dd1GUlyPEGKY+sdEIjKjs2bcP2Wl3MXD4MBgb6yP2Siy+mTgZpyMi6DsYpn6wZMuI3qcD+qKDmS1mrPgRTdTYxRxTP1iyZUQvOTEVb7Vrg6NHjqKHdw8aZZi6xZItoxIWLlyIi1EXcfjIYRphmLrFrqkYlUCWzsnIS+dbuUk0wjB1iyVbRmXMmD4Xcxf8yJ4kY+oFS7aMyvi0V09I09Nx7do1GmGYusOSLaNSRo0ciXXr1tESw9QddoOMUSlkysWOnTsi5sIFaGnp0CjDvH6sZcuoFC2tpvCdNAkzZs+kEYapGyzZMiqn/6BhiDoWgbj4OBphmNfvqd0IZEmRPxP/REZeHky1jWDjYAUdDdW65MrLkOFefiJSM/Kgp60HewcblasDIjk1mf8rhZGGNmydbUVTB6tXL8e0hQtw+2oGjI3/e+HIVGkyEpOl0NbQgJOzvcruB9LUDGhoS6CvYwZbWyv6iuqoqAOJhgQ27axgpvdiM8g9kWyPnTiG6NNRMNa3RLMWapDly5CRlQkPT090dRP/rElkWFBYeBiiosKhq2WOlkZGyC4pREZmJuxtbODp7Q1DfX36bvES9oPIaDRT14aJpRlKikuQLpXC1t4Onl5eDb4O0tLS8Gb7t7FzzSYMGDqYRquQ/SD89AmcCAvjT7ZGsDA3R4m8DGmpKbC3s4O7pwfMTMQ/XWN4+AlcjIqGXE0N1qQOSuTIKMiCRtMmGDywP18H5vSd4kVW/wgNPoTSB49gYmUM5JcjJTMVBvoGGDxoMEyMTeg7n4Ek2wobVm3g5s9fSEtVHj9+zH017itu0Zw5XGFhIY2K04Z1G7il8xfRUk1+y/y4caNHc9m5uTQiTlu2buFmzphBSzWtWreKGz1imCjq4MaNa5xTp46crLiERqps3b6dmz9nPi3VtHXrVm7YkGHcvfv3aESc9gbu5r6d8i0t1XTj5k1uxKARoq+D/YH7OW9vby4uLo5Gqty4eZ0b1GfQc9dBZZ/tlStXoGmgDnMzE4QeO0ajCr9t/g0ff/IxHNxcsXnrdhoVn4SEBMj41ouWoS5/Rj9Nowqb128GJMAYHx/s3iveOriSeB3lZeWw5Vtvy+YuQ05OFn0F2LNnD/KkWZg01RebN26k0YbL1tYePT29sWbDGhpRSEpKQm5uNsz5ltySJUtQVFS1Um/Anh2QZmRg2vRp2Lt7N42KD2n556bnotP/dcSsuXORyV/dViAtvYBtO/DdD9OwfnXD3w/+TUpyKqR307B42WIE7w+qUQfxifEI2BWAWYt/wLZtv9HoM9Cky61Y4VfZat2yaRO3ePFiobxlwxbuyNGjQpxYvnQ5J3skoyVx4Q86rpi2clatWsWt4uuAlDet21SjDn5e9HPl+8RmFd96v0vP1DEXYriZc2YLrdjtu7dzgUFBQpz4xe8XutWwkc9mZ2dbY5/esmUrl5+bL2yTOvj2W1/hWCAt2qBDVXWwiL8Cys7NpiVxWfXrGu72nbvC9jX+CoBc6WRn3+cOHz7ITfKZVNmaI1eCYj0W+JMp9/fffwvb5PPOmT1H+BoUGMjNn6nYJpauWML9dfu2sP1fKlu25Woy6OgoOv5HjhoFuVyOGTNmID0nE949qmZKMjQ2RBNJE1oSlwc5D4ShQYQP34KVSeTw9f0WxbLiGnVA+moKC/NpSVwyivJgRvugnF2d0ce7N+bMno20lBR89umnQpwwMzWrnKi7ISN9z927e2HTtp00ApTk5ENXX1fYJnUwsF9/zF44Q2jRfvpJtTowM0ZJfs0FJsUi70EBzEyMhW17/gpg+MihmOM7DxFRkfBb5VfZT2luYQL+5Cxsi829+/dhaWkpbJPP2/fzvvhl3i+ISbiKWQvmVtaBRQtLJCYnC9v/pTLZcmrqdEuhW7duePz4MRzat6ORKg/lD+mWuMjL5XRLwcu7FwoKctCqZWsaUZBI1FDGn4zESPKPaQPMrcxRLpPBxsaORhR0dJqi/B/11VCNHj2CvyyuuhQsbVKzEiytLVCa9QhtrWvegS/nDx8ZRLof8J/tUfkjWuIbGEamePjGQ9ha29KIgkSizjfMymhJXDQ0NOmWQgvTlpCrlcHayppGFDT4OpDxDbJnqRpnW8pV9k1t3rgZ8fFxWPDTT8hLz8Kxan24mZlZaKzWmJbERUtfq/JEsmdfAH8ABmDZCj/cuft3jT5caUY6DPT0aElc9Pmrmxy6jEzsxVisXL0a85cuhVxWhn0HDwpxIjUtDXqGzWipYXN0dOQTqhXGTRghjEIw0TatPBaSkxOxeu1azP1xLnKz82vcz8jMyIaBgQEtiYu2jjqysxRXb6SPduXS5fhx7o/Q1NPEgllz+X1EcVUjlaajpWkLYVts9Az0+GNdKmyT/WHlL/6Y9O0kaKhrCHVQ0Yd7995d2PCt/2dpNJdHNjSaNsal87G4GH0BLSxbYNDnQ6DZtCkcXJwReeYMMvgmdcbd27iflYXOnTvjjTfeEP4BMdHW1EbY0TAk/5WMcu4xJk2aBG0tbf7zdkFIyGFEXzkDTS1D4eaJ2ztu9LvERdNIH5GnzuD69eu4dDUO48d+CWNDIzg4OuDK5VgE7wuCsYU5rpy/ivc8utPvavicOjjhiyFfop1Tez75dkBY6GHcvn0HwQePYNz4r9DC3AwunVz4ujmLA78f5i8vLZD+dwrc332X/gviYmJihuMhv+POnTsI3BWAKdOnwtTUFPZ29tA3M8SW1WthzNfBxajz8PLyot8lLk3VNXE0JBQtLVpipf9KjBw1Eq1aWcLeXlEH29dvhdWbrXHx/GX0692Lftd/oH23gqm+k7j5i54+7Ml3qi/Xp08f7vZfz+4IbsjI5ySd30+zbNkqrr+3N3frr79oRJx8fXy5mXNm0lJNuw7sEvYDMdYB+WzdunUTtsnn/7c62LRqkzAciNw4EjOhDnyfXgfks/fx7iP6OiD5kOzvZ86doZEq5LO/yH5Q2bIlbKzb4uqlS9DR1YGZmeLS4CF/WRV17hTS70gxfqIPbGxshLhYWdtYIz4hAepammjZouryKCIiAgkJV+HRwxvd/k+crdoKNnY2uHLxCkofFsHAqLlwhUMur8+eP4srUdfh7uEK9/8TX4uutVVrBP62hf98nnBxdsGN6zeQX5wPI1oHRFR0FC7FnkdX9+740FOcLboKtja2uHQtBlmZ92Fmbl5ZB9JUKU6fPg0HZwd48nUlZlZ86z0zJxeywhK0tm5TWQcZGRkIPxGOt996Gx5eH0LyHFf6TzxBRvomSEXevn0XcsigLlFDWys7dPZwh5ZEQt8lbqQOzvKXi6lSKeTlMqjxdUBuDHRw6iis2KoKyOxYMTGXkJKSikI+4ajxv3pbK74OOnYSdR2E8/v+Sn9/HDx4UNgP4uLikJaSjtyS+1Ar5/cD27bo0EHcdVBdxX6Qmkr2g1yo8TuCkUFzODg4CnWhKhITk3Dx4mX+5JsNNUjQ3MjoheuATbHIMNWQK7mPP/of5s5fCDcXFxplmFfHZv1imGrIUuejRnyB3Zu20gjD1A7WsmWYf3jwoEgYcXPy1Knnn2SEYZ6BtWwZ5h/ICg7kCcK1K9fSCMO8OtayVVFkzmI8lEBdg790bqK4w0oev01KiodcXo6SkkIh1q3be8Jj3ORGyZkzfwgxQlOzGTp27Fj5iDd5vaxEBomOBE0lTSFp4DdTyePqjq4uWOP3K9zd3WmUYV4eS7YilldQgPzsbLSwbCnMZ0GGb4UEhyL2ymVIZIC2uR5cOjqjq5simZBkK01NFUZfaNG5AVpZtKj83pS0NCFGHuXMy8qBja1NZbK9knAF5yPPQ1ZUhgfFeTA0M8b4sT7Ca2QGqZzMHOgbG8LIyIj/Hi0hrszI5w3Ytw8TJ4zG5cvXK5+RZ5iXxZKtCIWGhyOK/xt3Po5PjDJs2ru/XocqkTHK69cHIl+WCMg04O7hBt+pDWMNsPfff1+YinHVKj8aYZiXw5JtA0a6AorzipGQEI933ukmzFhG5p+9cOE89JoZwcLKCs1NDJRmlrbSIjnu52egKC8P7R0cFDH+cn37bxthZ2OHtnb20NCRKNWyM/Hx8fj8s364EHOlckY4hnkZLNk2QGSynOWLl0NLoylMjVvApkNbOPLJS02t4d3vJJfrBTlFSEpNRFJiErLSMzF01EiY0On9lMHixYuhxv/5bvp3NMIwL44lWyVH1n9Lik9AVkYOPhv8GY0qEq5Y5xWuIM3MwPpfNsPIWBPOHZ1h18EehvqG9NW6Q2a4ev+9d3Hy1BmVWH+OeT1YslVS5GbV9u1rcDE8Ck5e72H6pGn0FdVDZoydNW06khOTsWrXqhde1bQ2TJgwGZ06OWH48OE0wjAvhiVbJVJaVoqm6op+weTkJGGuUJu2trAwF/8qrs9Dmp5Roy6kUimMTIwq6+x1up54DV+NGoc/IiOFp8wY5kWxZFvPyE2jhKRYxJw5j6zSPEyZ4stuxDyng0EHcfVaHIyNzdHt/95B2/ZtX2vXyuDhIzH4s8/g3dObRhjm+bFkW49Iv+svK5bA+k1bdPf+GMYaGvQV5kWQLpewsGPw8OgOM7PXdxWQnpqKD/p+hgvHo6FlqNYgb0gy9Ycl2zpEkuvVK/Gwb+uIpjqqMV1lfSBLkUeeOI1O/9cZDo6ONFo7Jk+cgMS0VBw9+DtLtswLYXtLHSFjYvdu24vd69ahMesleK3atm0LZzdXLP/lFwQEHFA8mlxLpk7xRVhwKPbs2UMjDPN8WMu2DoSFhSEqMhpOLh3Qw7uH6IdsKQsyX0NQ0H5oSLTw2ed9aPTVzZ08C/GZiTiw5wCNMMyzsWRbB8jqpBVzDDD1izxhp61hiCZar3ZR9/FHH2HGbF+4dWGT1DDPhyXbWkYO5pBD4YCGDMMHszGZyuZy7GWEhIbCy8MDbm5dafTFXYyNxfRvvsGJ8HDWd8s8F7aX1CKyCNw330yGXFaMwQMG0yijTMhCjlPHfo/du/di4cKFwkiGl+Hq7Ax5eTkSkhJohGH+G2vZ1hIyneHKX1ai3+e90a5texpllBXpzz12LBjW1m3h+JIjFjauXitMO7n458U0wjD/jiVbhuFlZGaguEQGa0vLF+oWcHBuj1ULfoW7tweNMMzTsW6El5SZlYnFP/700pehjJKRA2FBYVi2fAWKigpo8NkWz1mE9wd8hBtJ12mEYZ6OJduXQBLsj9O+w0effVyvk3IztcfM3Aw+U8fCsWM7zJ4x57nH5nb7sDvcXd2w/bdDNMIwT8e6EV5QUVERli9fjj4D+sDBVjEBNiMukVFRwhpk3Z9z7bHk5ET07fsZzp07X7lMEMP8E0u2L0EV5pJlXsyCBQugri7Bd99NpxGGqYl1IzyHi9GXhSkPK7BEqzpId8JPc3/ClYRYGnm6KVOmYuf2ncjKyaERhqmJJdv/QC4lAwL2ISbuElpZtaZRRpWQ9dAmfTsF4eFnERZyTFjG52nItJhjxo6F/6KlNMIwNbFuhH9BWjRLFiyBmY4OfHx9aZRRVeTEO3fWXAwfOwo2VlY0WhPZZzq/1REXbsUo1aKVjHJgyfZf3Lyegqu3otHzwz5sMm9GQG6OqjdV/89upJEjR6LHJ94Y0LtqvTiGIViyZZiXkJaWBr1metDV16URBWmGFJ9+8CEuX79BIwyjwPpsq0lKTsL6jetpiWH+nYamBpYsXSI83FKdhZkFvPv0gaurs/BIMMNUYMmWysjPwEa/tejTuz+NMMy/MzE2wfgx4zF/3nxkyGQ0qjB06GBcuhSHM2f+oBGGYclWEBsbiyVTZ6P/yEHsiTDmuVlYWaB3r/5YPXdujSFfNja2mLPMDyv91//r6AVG9bA+W97lyxfRtr0tu4PMvBQyCuFp+w6ZYPxbX1+4P+eTaIy4sWTLMLWEtGLTM9OFflvixrVr+GrqRBw/epw9CMOobjdCYmIqIiIiaIlhXt2DsgfwX75cGJNLtHNwQElBIW5L7wplRrWpZLK9fuUKlvnPhbm5OY0wzKsjXQl9eg3Cr6t/pRFgylRfLPtxAS0xqkzlkm0sn2iDjwVj8fz1sLa2plGGqR1u7q7o4uSG0aNHCxOS9/nsM8QkxCE8PJy+g1FVKtdnu23jNgwcNRRN2CJ9zGtE5jxupqkrrOJ7LPQY/vfR/3Djxk3Y2ral72BUDbtBxjCvGZmS02+5H6KjonDw8GEaZVSNyjTvnnfmfYapTaSFu9V/HXx9fXE1Pl5YgZlRTaJPtqRVsXr1elyKukQjDFN3mulrokxdjtDQYHw9zgdr16+lrzCqRvTJdsPaTTDS08b/uf8fjTBM3SHja7/44iukJqZCz9AAQUFByMlji4SqIlH32R4LOYaychl69epNIwxTfw4cOojsnFxcib6MtRtZC1fViDrZxiZegzNblJFRIkVZeejQuSNu3boFiURCo4wqeGqyJf2chXkl/JYcauWAvomxyg3IrV4HZC4RY2NDqKngcLG8ggLIy8qEOjDh9wNVVL0OamM/+GbyRNjZd8Lw4Z83mIRbvQ4MDfVV8kRRxNdBiayM//3zOVH/xevgiWQbdvoEoiMi+Qo1g7qGGh7KHuJ+Zjb68ZfiDi6O9F3KLSU5FdY2T1+65FnI8+3hEacRfSIC+mb6fB1oCnWQnXUf9s528HqvJ3R0tOi7xYnUwemoSESdCIe6RAOGfJItKy9DulQKN7cu6NbtPZVYsjsiMhLhp49BE9ow5vcFmbwc6WlSOHXpAM9uPZ6YOPx5/f7775jqOxUxZy5AR4lnmSP7QfTFaJw9cQpvoBF0TQz5mBxpyWmwtLLAkGHDVGI/SE5NRfixYyjgk62hviHK+AZYekY6zAxNMGTIsOffD0iyrbBh0wZu0fwltFRF9vgx98WIEdz8RYu44uISGlU+skcyLuZCDDd//nxh+2Vs37mdmzdnPi3V5LfKjxs/fjxXWFhII+K0d/d2bs6MObRU5TG/H5A6+GLEF0q9H9SGwMD93IwZM2ippk1bt3JfjB7NZefm0siLIfvmu17vc+916sQVP3pEo8onMCiImzn1W1qqKSYujhsxbASXn59PI+J05MgRro93H+78hfM0UuXGjevc6BHDnns/qLweIuNQM1PTIc1OE8YGVncrIQFWjpaQFRfj5MmjNKp8yuRlWLhkIT7p+8lLzbJEPndK/FXcz77Hb9ccD0nGR0YERaBNqzYI/SOYRsWHTKJy/sJVZBdmC5P1VJeSkiTUgWtXN+zfuYVGxYccCxdizqOksARxcXE0qkD2g9DgYLz1ZmucCztFoy+G7JvfT/0Gpy5dwqGAABpVLqQOYi6cQ76s5In9gAg/E4Kurl2xadNWGhGn0NBQ9B3VFyGhx2ikSnh4JNq3d8ah4CAaeQaadLmdu/dyV69e5a7eTOCWLJzP3b+vyNZ3793lZvjO4PJz87lCPjZn3jyhhaOMlvot5Y4cOElLL+73owe5C3zL+M8//+TmzJnH3b17V4iTM5fvDF/u2o1rQquEtJyVtQ5e1d7AvdylmBju1l9/cT4+PtypU6eEeHb2fc7X15e7deuGUAez58wW4mJ08vhx7uSpP7i///6b853qyx35/YgQJ1c0vt/O4GKvxQrlmbNnvPQVFNl/lvku4Dw9PWlEuRw/epw7e+YM9xdfB2Q/+OPUUSFO6mDmnDnc9i3bhSveefPFux+Qz3/0qOJ3v3PnTi5wf6CwTa7qli5ayq1bt0Yoz5k3hyssffbVbmWyXfzzT3SL4+JuxHNffvkl98eRo3yi9a1x2bxu3bqX3sFet/Pnz9Gtl7N8yXK6xXF/8clm0qhR3KHjv3PzZs7m7t5RJF5iza+/cvfuvdwlpLJbyJ9kqv9+V63z4w4FBXMzfWfWuFzavnW7aLsS1qxRHEQV1q3bwAXt5y+p+UZH9f1gw5p13O1q5ZfRs08vPrmH0pLyWMInk9xqXQTrVm3g94MgbsZsX6GrrkJQ4H7u9u3btCQu69ZsqHEskO61iu6lc+fO0CjHbdmwnTtXrU7+TWU3QiMNDboFONq2x7Tp07FrTwC6e3nV6ARvVu19yqZLFze69XKKZcV0C7CyssJYX18Ebg6AnVMHmJmb0VcATQMDlJQU0pK4lKC8RhfMsEFfIDjkEFy7usJQv+pmjnYzTRQXV9WXmMjKyCiUKv369+MvI4Nh/8/9QFODf2/N9cde1KJ5y/D93Dm0pDzK+T+aWlXH+pARA/nL5RB0sHOCs6szjQLqujooFumxUI6yGseCd8/eOHHiBGzt7ODmVrX6hpGpHu5l36Glf1c1hkX+uHI10IOHD2Lbcn/87PezMNt8ZFSUECfSM7P472pMS8ohMTmJbr0aY2NjYcgXcfjgQWzevB7LVvyM9PR0hIefFuJEZloq9IyMaElc9DQ1hbuuBOmfXDh/IRb8tADSNClOR1bVwZ2790Q7FEyvmRGKihRzaZA6WPmLPxb8+BMK84tx7FhV393d+9kw0NSmpZfTvr0Nurh2wc+LF9OIctDQUUNxjuJEQvpvFy1agrlzf0BxYTGWL19SWT/ZUilatmgtbIuNgZ5B5erJ5PMuXboU338/HeVyORbwv6+K1+7cvgMbCxth+79UJtu3WrRBUkKiMMwh5nwMFqzyg7GhMUaNG4VDQYHCzSOyAq2spFippickNzCO7Pqdll5N27ZtcS7iHOIT43HpQgyWLV4mtGQmTpyIoKD9SEyME24gcY3egL5Ih3+1a/82rl69CmmqFEOGDEH/fv1hZmKGsWPHImTPIeFmCTn4CrL4k65IWVtb4fz5s8KxMGHCBPTq2UvYD8aMHcUn25DKm2YFBXnCsLhX1adPP6zbsEGoV2XhZuuMqwkxwsmm90e94cVf4VpaWmL4mFGQyeTYskVxgzQxOVG0QyGNTUwQeSlG2Caf19PTU1EHw4fDTMcYGzf/JryWnpEGe3tbYfu/VI6zJc9rr129mr8sKsPXX/sISzVXuJl8E7u37YU6f1Xhwl+q9/D0oq/UL/L//MPkyRj13TQ429nT6MvL4Vt0/kuWQqKpjjEjx9S4ZEzmW8/+65eipZ4dHLvY8nXQg74iLuTqZsmSRcIYa/euHjUWK7yZkoJVaxfhrZYOaNWmNXr36kVfERfSilmyZDk01CXw8HSvccmYlpaG+fPn462330b7du3h7V07+4GjiyNmT/JF36Gf00j9Ild4836YD011dbi6ufDJ1pu+orB+81o8KHoIKzNLfDrgUxoVlwcP5Fi+9EcYGhtCAk2M9RlDX1HYtWMHsvJyYMHXQd/Pnl0HlU1U0h/n/UkPqPP/bHFuzT6rkoISqEvK+QPPQ2kSLbF+7VoMGDWqVhItYairi0Ejh/CXCUB+Yc1+KHIAmmq/CTMLA9EmWkJLqyn6D/4cZcXlQrmia4mQ8XVgY2zPv0dLtImWIPcoho8cLDwpRFpxDx5UtThJF4utrT30m2rVWqIlFiz4GRP4S1Ry9agMSF/lKKEVK4NEolFjP1BMjK4H9cYS0SZaQktLwu8Ho/irvAxo62lUdp0QpA4kmhI05t5Az76f0Oh/e+IJMtJaPBF2DKn30qGl1gSPHj6CTVsbeHh4CgeiMomKjIJb11e7KfY0pA5Oh4fjzr07UCtXq6wDFxcXmJlVtXbFjNTBVf5yOSkxBfJyGX8CKkfLVq35Vp6rytRBQV4BLlw6hz8z0vEovwScmgRmpgZ8i7/7a6kDz+7d8SnfQvLxmUQj9Y8kmEuXLiEpKRFlZXJw5Rz0DfRhZ28PF+eqG2Vid+3aNVy4cEE4+Tx69Ai6uiaw72ADVxdX+o5neyLZMgxTPwK2BWDgiIG4e/euypzQVAlLtgyjJB6Wl6NbFxe42rtikd9SlZh3QJUoz7CCF3Ag+CDdYhjxIKN8jhw5iRNn/8De/c/5CCjTYDS4ZEtm9EpPl9ISw4iLsbE+ps78HpsXLUUGHcfJiEODS7aXL0bhfz0+piWGEZ+BA/ojJS8N8XGKMZ6MODSoZEuGW1xNTICN1cvNVcswDYGOhg76DR6CE+EXaYQRgwZ1g4wk2/zMe7Bp/+ynNRimIcvJycL773+AMUNHIi0vHdJkqdAyMreyQFuLDnDv4Qob62c/IsooDzYagWGU0K6APZg/Zz6fdKVwc/YANOR8VML/AWRyOdT5r/0GDcHgwfXzxBlZxUEVl4l6FQ2itsijgzl5ObTEMOJGJicP3L4X1pZWQL4cCWmJfFQizMtBUi5RLpEgMHAvQvj31jVyhem3eoWwLhnz/BpEsr2d+hcOBR+iJYYRL/KE0rYDB/ikKoeGtgYc3N2Qli6tXFyQJFwNDQ1F4uX/7uPfW9cT2Ny58zfOHTsPSZnikW7m+TSIZHs59grcXLvSEsOI166AAJTcuyckV5J49fT0YKCpV5lwK+IV29nZ2bj3Z90PhZRL+Da2juqtsPsqlL7PtrRIjqXLf8IPc3+gEYYRr759+1a2WkkyJV8fPniAmKtX4eammAeEtGwrEi7h6eWFr318hG0iMjoSG9duRM+e3jh77hzSpekwMjCAc5cuGDJwkDDHCZkDevOyFbBo3w6xl2P5n1OGFSt+FeYoDgs7gQP7AlBYXAhtDW2YWFpgzMiRwvSCmzdvQ0REGPKzi2FsZowvRnwhzE9CuhY2blyLxMRE4d9qpq4H167OGDJyhDCpDfl5ixf8JExklZSShISEBGiqa6KdQ3uM+GJEjVkGxUrpW7Z/3klEl64utMQw4kUSFkmiT+Bzqow/VHMKai7EWiEvr2ZcLpOjmE+Gu3fuRb9eA7F111Z8wifx8KAgrF63RvEePiGm3slGZEQEvp4yBV9PmgQ9Y0P4r/bHxtUrMXT4cKxZtwWTpk5FfvEdfP/d98KkNP369cZg/jXy/zR79kx0cHLC9es3MG7EaOTn3sfPy37mv28DxvqMRURUFLZvViwI+fBBKe7cuYPg4GB4eXhhzZpN8OzphYsRFxEaEiK8R+yUPtna2tjCy7PmXJoMI0ZyuUxItqQ1S1qvZNmh8LgonDx5BtqSMlg2qVqWiKho/er+Yw4FMlIgX5YPOyc7uHu4CeN2vXv0gAPfMk64VrXqCp/B0aFjJ7g4OgqrRRTmFCA4KBjdvbzRtWtX6OtqoT3f8l21bBPk/JvJpOm6urow1jcWfraBiZHQSr5w4azw88aMHStMNK/Pv4csnTN86HCEhIcLP6q8rFzoEiHzYbu5dxWelOvh2ZNvpgMpaanCe8RO6ZNtxaUSw4gdmemrZUtToQVLEtvF2GhYaZihc+d3hOFfMu2ax0JFN4O6es04GZJFkrUwmqGa9z74H7LvyfgWNF1lg090JKFWSElN4kMaaNHKlEaqWJhb8a+n0FLN4zI9IwMtjUxhamlNIwpmFuZQL5YJjx2rqasJJ5Lmps3oq2TpHcW/QT6DKlDqZFt9wmKGESsytJHMlzpy5EiEnQ1DRmIqmhs1h7trd1jZWsHQkG/R0rUXSZKr3l9LEhXps/0n8h7LfyRbfZ2mwuV/fmE+//3qkPOtUYmkag21wvx84atO0yeXudFopoky2T+S4kPF/0PhvWLoGDeFulrN2z962s1QwreJy8n3lfP/hvAZ6Ach6Pcr/it+Sp1s1671r1yAkWHEhOzXZH2vbds2473u78N3mq/QT3rrQgYGTx0LEzMTIQuRFmpFC5YgXyuGfhEdO77z1CfJyHvSpGm0pCCVKkYttDBtyX9/GSQaevyPqEqgLUxbQMb/IUu9/FNeeg4MDKpapWrk5zdRfK+RtRGypI9Q8qBmf3NGpmIiHT0DAyHTkO5oteqZVVKm+FquGulWaZNtRgZ/qVMmQWMlW8mXYV4FuckUELAL73l+hL4ffoTkhGQcPHAAR8OOwqN7d76FKMHU8ZNgatq8shVLVCTcihYtYdqiBXx9n1zVQa1cMf41IjyicimX5JRk7Nq8DZ07vSP0s5KWrdA/LLyqYNOuLWxtbXEiOLhy5ViyJNBm/oRw5/4ddKm2Kgp5qEJepPg5LvbOKC7Oxt6dO4UyQW72nQgORad3Olat8EI+ilq50KcskJPn4PgvNf4vxEtpk21oUDCcuzizRwIZ0YhPTUXHVnaYMGQ0FvzwPaKuxWLBz4thYlJz2BNZD5CsSaahp6dIiHySrd6izecv97X1tDH3hx/4RPaUCcb5REjeW5hdiBkTJiAoNBgLfpyLO9n30NNbcbNZwl/Xa1jx/3a1BxPIEK1lq1ahuEyGiaO/Qmh4OCZNmoLQ7aHo9k43WJhZCO+zdXLif4Qck6dNREREBDw9veD0jhP2BwVh1vRZ/MnkAMaNG40zF87By6On8D2NmjTiPw///5/LJ52KY5q2jCUq0rJtNJdHt5UGeQxwud8y4W6mTjM2Wz3TcJGbQ+vXrsPkyROwP3A/vvr2K2zatQu2b79N3/F0pDXYlW9JmpqbQEPCJ6nHZXwCbQJ7Owd4fegFH5+vYdK8OX13TSl8Uj/LJ8F+g/rgsUQLV6MvooOTC2bNmom33n5LeE9hYRmKUmVwcGkPq2qz6JG05+ziivt5OYjh/w2LVq3xUb8P0a//QKir06tMPuEXFpcgOyMb1tbWeNPmTbh7eKC5sRFupl7H7aTbaGndGj7jx8LVtZPwLcX5JSgozIdTJ3tYWLQSYnhczreAs2HJ/3wHh9pZtFWZKeVDDeQy40HZA2HICsM0NBmZGYiLuYRdO/YgITEZg4b3w8ghY2FoqPtKV2qkDfo83x3Ot0iXL1yOSb5fw8tLvCtBNzRKeY1OdkiWaJmGJiIyAqPGjcEH77+H4OBQjB07HleuXMZ3U6YL40pftUus+ncXFT2gW08Sfo5w07+qi4Cpf0qZbBmmoSB9qImJqRg3YQTe7/Y+jKGF69dvYt26dXDv7k7fVfuWL19Kt55Eki3ps9XQqBrWxdQ/pUu2pI/rtx2/0RLDKCcyBvxY6DF8/PHH+GTAR+AeNsG1G9exeJ0ffcfrpamu/q9THJKnv7YGBKCzW2caYZSB0vXZngg7IdxpJY8PMowyIWNjzxw+ibBL4QgNDUbnjv+Hqd9NQXtbB/qOunPw4EHhxpKzoyONMMpO6Vq2NxKus0TLKJW0tDT8/NNidHbpjIBjB9DJqRMunb+K3377rV4SLUHu/ickxNMS0xAoXbLNLVA8Msgw9Y08WLN8+UK82f5t7DwUiH18a3Lzxs0YMGBA1UD9emKoq4vu7t1piWkIlKobgVymxV2+hC5d2EThTP0hc61u/m09Qo+dQMeOnfB5r1744JOewqB/hnlZSj95OMPUhWvXriMuLgY7d+7EY/6QGDl0OIYOH0pfZZhXx5Ito7LI2l3BB4Owc/tePCx9CNcP3DDm06GwbteWvkO5ZaRnQJqZBldndo+jIVCqPttfV/ihVK4ak1Iw9YMM89+3Yxf+99H/0MaiBeITUrF06XKEnw7H4pkLGkyiJbSbNUPkmYu0xCg7pUq2uYX5aFptViOGqU2xidfg4uaMr74ZhxHDRiMrqwiLF8wVViNoiJo2bYKSglxaYpSd0iTbPJkMhro1l/1gmFeVk5eHjat/xfDBgzFi8CD08vDGzVu3MWBAX/qOhqv6dIuM8lOaPtvwiEsoKv4bn3h/RiMM83LI010hIcE4ceoELpw+h97DRqC3pyccXRxfeX4CZXPx8kV0cHZBE5F9LjFSmmQrTZVCXVtdJZY0bkgiTkdi2ncTaakmsvDfkePHaan+3Uy+iaU/LcGpM2fQp38feLp74j2v99iQLUYpKM3p0MLKgiVaJRQRE4m4S/HQ0dGHsY4ZLHSshK/kr62TcsxBmpGfgWnTp8H+LXvoaOniwoUYLFu8DD28e7BEyygNNvSL+U+jxozFhfNncf36DRpRHsfCQoU5Y0+cOwavd3vBZ8wYuLqp1jAo8iDQvfR7sLS0pBFGWSlFy1aaLhUmPGaUT1JiPDq7v76pAl8UWSRxwYIFcGjfDgH7D2DMqLHI+CsL237brHKJliCLLO7bs4eWGGWmFMk2JTkFicmJtMQok8SYBHTt1JGW6geZKHvx4sVwdnbGJ598BH19fZw8cxa/bdgM9+6q/Wi3vq4uiktqrmrLKCel6EYIPRAMszYWcHJyohFGGcTFxQkJ7p33vGCm/+RE1OvWbRJWIHhdyAqtGzaswebNm4Xy/iOH4FxPs2wpM//l/pg09clVdhnlohQt28zCLLxp+yYtMcpiwYJZwte0pCtC4o06fUn4Sv4mJSW+tkRLpjT8/vvv8MH77+LGrVuYMXsGEm8lskT7L9S12XjbhkApWrY7ftuBoSPZpB/KhFy6N29hCg2JBPey7tW4q/+wvLzWx3VmZmVi4+qNOB9zHll5eZg0fgx69eoHHR22Ft2zkHHF9T3lI/NsbDQC81RXrl2BUwcnDBw4BHv27KDR2lVaVorzkefwy/JfUJCTCa/P+sH7XU84OjuL7uEDhmF7NPNUcecuCF+7uroKX2sLaYWFh5/AhAmT0a1rN2z+7TfMX7gQp6MvY9bU6XB2cWGJ9gUVFRUJ/duMcmN7NfNUMWmpwldT6xbC19pApjQc1P8TvP/+B8jIkOL3w0exa8cuODo6sh3xFZA+dHIjkVFu9b6PkwNw/er1tMQoi1uXY4WvbVvbCF//iQymfx7kfdu2bUPfAX3RyaETOr3jjhs3buLAgQMwMzOm72JeRbNmzXDj1jVaYpTVU5NteXm5kATz+EsTslwyKb82pWooK1e+cYIVdUAuz4r4Onje5CIWu/bswv37ubB+2wZ5eUVCHVT3xcgvhFEDTyOXy5GSnIqJ33wFJ+dOSEy8iplTZyKGb4HNmjULtrYNZ85YgvzuK44FZdwPJBJ1yGUar/X/jfzb5FggdUCOC1VUfT8g+/iLeuIG2cXoaISFhUKiaQL9phLIykvwoKgUvXr1fi3zfpJfYGDgbvj4+NBI/bt88SKCgoNgomcGDV1NlMlKUFBQBDc3N3Tu/I5K3Pm9ciUWIcfCUC6XwcTEHLKSQuTx+4E7XwcXoy9ixswZGD9+PNasqbp8TUxMwp6APQgJCoRGMwNMGv81evbu1WDrKzb2MkKDT6AMJTA3t4C8tAwFhQVwdG6Pbt3eU5qREskpyVj8w1ys+m0TmqrXXl2TBseVa9cQfuwESsqKYWZO9oMSZGZmwMa6Lfr0U43RIllZGcJ6dGkpKTAxN0Fp6UPk5+bDwtIC/fv1f/46IMm2wq2//uJGjRrFFT56RCMKhfcfcX36eHN37/5FI7Xn/v273Kp1q2ip/sVeixXq4J8KSws5H59R3KpVfjQiXnfv3uWGDRtGS1VIHQwa1IecnIW/nTo50Vc44XdIYt7dunF3S0tptOG6duMa9+WwL7m7eXdpRIHUwcyZMzm/xcqzHzzij9fY2Fhaqj1kPxjUqw8t1XT8+HFu5pw5tCReJCd6eHhwe7ceoJEqR44c5ubPWURLz1bZjUCayLs2bkarlq2hjsc0qlAueQBb+46YPn1WrU9Ioqmph/e6v0tL9YvcKd+3Yw9atmzx5CXZI0BP2xTXr9wUWn1iRT732tVrYWlmjqKimne470rv4lLoJVoCLl2Kw4ABn+Mth3aIOBaJ438cR1D4HzDT0KDvaJhIHezbsQ8m1saQPKr54IbaYwk0tLVx5eYVoeWrDMgk4rX99CWpg40b18PC1uaJ/YDQUFNHfna2sJyQWJE6CNi2C7a2ttA3a0ajVTQ0muFeegqio6Np5Blo0uX2B+7nLsXEcHE3rnKL5s0TzuAE31zmZs+byd29c5dvhZZy82bPFOJiFHL0OHfqzBku5vpVbsn8+dx92kLLzs3lZnw7U2jtyB7JuDkiPqMfOnyIO3PuDHfzz1vcl19+yZ07c1aIkzpoa9O2slVb8XfYkGGV+4pYnOX3gZAjIVw8fyxMmjSWO3tWUQeFhXyrdrYvF3Mhhnv8+DE3Y8YM7rHwivj8ceokd/SPo9zft/8WWvgnT54S4sXFhdyqZZv4K7xVXAnfop4n4mPhLH8cBPJ5kVw5rFmzhjt16g8hXlxcIlzhkhj5/c+Y6ftEb8DTVCbbn5f9LCQSIiH+T/4ychB35tQpbvaMOUKirUB+QMX7xMb/l+V0i+Ni4uL4ZDNMqIN5s2fXqIMVK/y4e/fu05K4LJy/SNiZKvgvX8odP3mSe8fj/55ItOSvnp4efxLOpe8Wh1/X/Eq3FJfoy/k6OHnyD27O7JrHgp+fn3CpXd/ISWDVJj+uOP8hjby6pSuWcrn5+bSkOO5/J5fNC+dzx48fEU42xKHAvdztanUiJlu2bK15LPj7c0eP/8HNmzeb3x9O0ijHbVqzibt27QYt/bvKbgRNDbXKRzLbtbfGNr75TAac9+7dC2bmZkKc0NTURJm8jJZeHblBFhERQUv1q+hBKd0CnB0dMdd/PfyXroRnD88addCihSkKS4ppSVxK5LIaN7QmfjMN25b443z4ORqpKT8/H0smf0tL4lB99A25RP+Gr4P169fCw9Ojxn5gqmeK7PxsWqo/MlkxwkMjUFL2gEZqQQGgo6VFCxBuhv4ecIQ/Lhzg5eVd+eCJjqEx8gvrvw5eh/LyfxwLEydif+BedO/uCQ8PDxoFrNpaIT45jpb+XWWyrZ5oyBMps+bORRdXVxw7HYqHD6teK+f/qEvUaenVyfmDOzVVMYC+vqlrVH0u0n8btHk9Or7bCacjImv04eZn50NDXZyTf2hCUuOznjhxAh16dMeEr75CTEwM+FYNtmzZwJ+Ee8O7pzdsbGwQHB8lzKUgFmqo2eccFR2FTl3chUYB2S8qFMoL0Uxbj5bqT8UoJA31p47kfCnl2hDuulc4fToSVvbWiIq6KDSQKhQVlUBbXZOWxOWfo7vIem9OTvY4feK0MK9yBbLd0siUlv5d5W/HzNhSGBtZkFeAJQsXCauPjvfxQa9PemPpwuXCAUjGlknT0mp1qRF5uRwS+Wscx/sCWpm2EMaOkgNqyZJF6OT0Dr7/bjp6fOyNX/yWo4juZBkFUpibmQvbYmNuZYa/kv8WTrj8ZROSk5Px3ZQpmDB5IoJDQvid7R2MHDkGnTo54cjvR3Dr1i3ciL0GHZ2qVlBD16qlqXAjmOwH29ZvQ9T5SEybMgm9+/bCLyuXVyabdL6RYGRW1dKtL2pqihP/i4/8/HdW/P6dmpoi1MHq1euRfD0W3/Et/DFjxoC/jBZOwkRS0g1YWVsL22JjYWkunGgJkmjDw0/Bx2cShg4fjIULF/Ll08JryclJcHLtJGz/l8pxtmTWpV07diCbb7V9PckHZiZVO9H1xGs4FBDMX1PJ4ejQBT179aCvvLrMzCwcCgrG2PGjaKT+ZOXkYO0vK1GuUY7hg0fCysqKvgJcjr2MrVvWwd6+M1qaW+Kjnl70FXEhSXblGn8UF5SgR48ecK+2SgNZUHGV/yo42dtDz6A5+n72KX1FXEiDw59PqhKJBuwc7fCJ9yf0FT65XE/EipV+cHZxhKlJC3zSq+q1+kLGvX711QR+/9wCHV1dGn01QoNj6SJoqKmhvYszenr3qvEE1PrVqyHnr3Cb8VeDQ4cPp1FxEY6F5f4wd7CB9Foyf7WvmHK0wmq+DsjVsIaGJoYOHkyj/66y/shii25d3GBgoI0yWc0+2UZowp81y+Hm5l6riZbQ1uZ3aL5p/jJPZNQ2Y0ND9OrTiz+naDwxGYpWUx20bvk2SkqKRZtoCTJAu8cHPYThTdoa2jW6FBrz+4GtrT0KZA9Em2gJXX1d9OzbD+VlajDW069RB2qNNODg4Iyc3BylSLSEtrYeZvrOrLVES5C+yv6ff44yvg6M9PRQWq37hDxBZtqiFUpL8kSbaAlyLPT+vDfiwi7Bnj/pVu9CIsPhWlpZIy89A4P5enoeTzxBFnsxFv6rl8PCwkroj5Pyl0rJ/F/Sh2tTraUnZqQOlixfKBxULVu2VNRBYjImT5+mMqtJxCfG860XfzwqagQ3D7fKOhgwdhS8q90cELO4+DhsXr+6sg4ypFIhNnysj8rUQXJyIvz9l6O09BF/leMh7Aenzp4VGiWT+EtqVeHvvwQ3Yv+Cg5sDSvNKcfSPo/Dy9oDv1Jn0Hc/2RLIlyLO/qUkpyC3MRjP+rNbB1gVNtGqv870hIHVw5/ZtYXYqPQMjoUWnowKP6f4T6cdPk6ZCU1sTTh06oEkT1a4De7sOKvG49j+lpqXz9ZAA7WbNYG3VFoaGuio3FWZqWhrS+JMNGSBg09YWzfg6eJFJ9J+abOsSGWaTxrcYrNhSzAzzUjL4S9nEpMQaw5EY5aMUp6bNv22kWwzDvKik5CScP3+elhhlVe/JllyKSGp10ArDqBZydejkZEtLjLJSipatpoYR3WIY5kUVFORBz6g1LTHKSimSbVMVvOHAMLWlaRMt2Ds8fUUNRnnU+w0y4sGDImhpsSWrGYYRL6VItgzDMGKnFN0IDMMwYqcUyVYqlQqTnlR/LJJhmGcjD9/4L11OS4wyU4pkS+YMDQsLQ0leCY0wDPM8iosLoa6tTUuMMlOKZGtGp6nLLc4VvjIM83ykqVLYNbCl4VWV0vTZkmXC06XptMQwzPMgqySYsUfdGwSlGY2QmJwMrrQc7RzYWZphnhdZ5aSFRYtandCfeT3Y0C+GYZg6wIZ+MUwDxkbwNBxKlWyj4uOUYsUGhmkIyFpoJ8OO0xKj7JQq2aZduYGMzKpVKxmG+XdkQvOKxR4Z5adUydbF1RWXL16mJYZh/kt8TJyw2jHTMChVsjVt0QJJf8fTEsMw/yUtUwo9Q01aYpSdUiVbHR0t2Fm70hLDMP9l5NDhbMhXA8KGfjEMw9QBpWrZMgzDiJVSJtuEhAS6xTDM0xwOCRbWHmMaDqVMtgcO7qNbDMP8U5FcjtSkP4XFUpmGQyl/W20tbJGYmEpLDMNUF7h+G9q1fpOWmIZCKZOthbUFNm/zpyWGYSo8eFCKiIvhsGjHJmxqaJQy2dp36ICivFJkZmbRCMMwRJm8BA4Ormhjw5Yub2jY0C+GYZg6wHrYGYZh6oBSJ9vSIjmbQo5hqIK8AuTk5dES09AodbL9+04SQkKCaYlhVNvuwN0oKS6mJaahUepk26ZNGyRcYw84MAyRmZ4OCwsLWmIaGqVOtk2aNIW1dVskpyTTCMOopojISHTt2p2WmIZI6W+Qubo64mL0RVpiGNVUXFKIDk4daYlpiBrE0K+H5eVowh5NZBimAWPjbBmGYepAg2kuRkZF0i2GUS0BAQfoFtOQNZhke/XsOTY5DaNSyErTcXFxyM7OphGmIWswydamUyfs2rVZ6L9lGFVQWvoQfn5+6NaNLeooBg0m2Xp5eAAS4ExoKI0wjLgFBe3HRx99BAcHBxphGrIGdYOsKEuOqynR6NqlK40wjHiRFUvs7OxoiWno2GgEhmGYOsAGrzIMw9SBBplsr1y5wh7hZUQr+mIU/zealhixaJDJ1sLSEgf2HaQlhhGPIlkRwkNPw96uA40wYvGvyZb80snf0rJSGlEehvr6sDI3Q+TF1ztngjLXQV0hn72iDlR16ezqdfA6kbmblyxeAmc3R2hpNaVR5VBXdaDMKutALhfGQL+op94g27VtF0IvnYd+qYyMtoL7R73Qp08vxYtKgnzYBYvnYu6sBTRSu3bt2oXz50/xNQxIJBK4f+jB10F/+qr4kfpNTpZi27bVKM7KF2LuH3qhf3/VqQMiMTEO67cFQJ6leLDgddZB7MVY7A7cgmXLVtGIciAPE23etR6yDEUd6JmZwsfHB2ZmZkJZFWRl5cHffwnyaR2YtbHCF1988UJ1UCPZklngV6/0h529Pd568y3oaeshp6gA8VfjkJmdieFDRsHYWJ++u/4lJyfCyspGSIa1hdTB2tUr+X/XFg4Obwt1UPCgCDExV/mfFwPvnn3g1sWNvlucCgoKsHLlSujzv+uOTh1hbmyOBw8e4AK/HyRe4uugXy+4d3Wn7xanoqIi/uDyh35THTh17gRLS0vk8fVy9epVxMfzdeDdG+7utTsEkfxMyJpCx7j29udXQVby9ff/BbpNtNDx/zrDxMQMD/nY3ft3ERkZCVf+OOjh5UnfLU7kamPr5q1IT0+Hl6cnLC2shHxw//49REVHoqubB7p3f779oNFcHt3GgnlzoN5EB1+OGQ1TU1Po6uvC1KS5MIn30cO/4+DhfWhr7QBjE0P6HfXL0NAYarU4Gxip2OULf4L8cTnGTfgSLcxaCHXQvLkxbNu/hYuXr+Hs6ZNo1aoNv+M1p98lPj/++AOaNGqKL32+hLWltVAHRs2NYGP9JuITr+P0qRNo0bIVXz/ibNmQ7pLFi3+GTFaKCd9OxJtt3kQz3WbCftC23VtI51v8waEH0bp1G+E4qS1NmjRBEy3luI1CntQkx0KB/AFmzpyFli1bQl9fT9gPrKys0IhrhB37f4NRMxO0shTvhOY/LliAzFvJeN+7F7q/925lPiB1IGnSFDu3b4W5uRnfwm1Bv+PfVf5mDwYfRK/e/D/o4Q6/lX6VfRLkbLtoySJMmfotf3mzDIdC9ild313sxWuKVsErOht+Fl35M3Xvz/th5bJfhf4Zgpzh58+dD3c3NyxfvhLHgsW7VE9oSCg8vXui94DemDZ9Bq4kxApxUgeLFs3HO++8Az+/NQg5JN46iIyIQCfXjhg0dCDmzZrNl6OEuHAy/nkJjKxMsWbjJgQHBdfKGnlZOTk4ceIELSmHC1FRcHVzwfiRYzF58ji+oaG4P0L2g9Wr1+NyQhzW/LwGJ8LDhLgYkREhHeycMWf1aqQm842M04rJsMjv/MCuXYg4Fy7kykPBoZW54r9UJtvbibdh59iBbxa7QVdiAtLgJf+AP/+D+vXqBzM+exsbm0GtSXmttiZrQ2rqn7h06RItvbyExAR4dveAs50j9HVaYMa0KUJ869bt8PLy4i8b3YUbF1zjRs9VuQ1RfEI8OrV1Q7u27eC/eBl2rtkufNZNmzbwddCjsg6MLZWnO6m2JSelwJ1vdLS3dcDUWb7YG7hFUQfrt8LOpQs+8f4ETSWkFdoEZXmN6He9vPAzx6Curk5LyuHShXNw6vh/QgvOz28dAn/bLdTB/kO7kZEhxYSx49FUR0t4XazHQkJcAtzcOkFHIsHAMeOwZ88Ooe/2UMB+BJ0/j2lfT0NT9aYw0THBndRnTxZUmTXL1Eugo6EjbA8c0QdWtrb4Ze4SmPGX6s6uzkKcMNEzr5WzeW3q2ft/CI84LZx1X0Vpte8fMv5zvOf1AaZNnMiX5OjatapfxsjAALn0ppHYPHxQBC1DxW6hoaGBYRPG8kn3F8VNQj7RVmjRrKWw44mRrKzqWDDTM8O4r7/Fku8X8qUS9PB4V4gTpkYGyC5Jp6WXQ+4RJF3nk3u1ulUGjx69AW1dDVoCfKZNwvIflyInM09oiFXcJzExMcS99HvCtuhIyitvgJGE+/333/NXtksgzb6HdXP8KuvAtLUBpBnPHvdfmWwbcTXPrPJ7d6Bu3AwFspIa3QZyJRz+Q9YqG9inH98C2U0jL6eJpNpwjtKHuCe9B20DUxQUFeBR+SP6Al8HahK+dU8LYsN/tuofriSzCDr6Onggrzn0S87/UeN3RjGSo+bnKskrgMRIkz+51DyZl4PfD/7x3he1e+dWDB06lJaUh1xezh/rVcdDRlYB1PU0UFYmoxGFh3y7i9SCGMllZXRLITMrE0b8CbYsrwgyVLXmyXEhkVSdmP5NZS3pNNVEalpa5R1I+3few/Sp38HV3gm/rvarPNAyMqVorNZY2FYm7R0c4Fat9fkyDMytkZ6ewddBERYuWQJ7/rP/8MN0ePKXz2tW+CFLptjR8tKlaC7SG2QmFuZISUoW9oNtuzYjPjkO43y+Qq8e3vjZ/+fKS8akpCQY6ivHjdLa1qZ1GyQmJinqYNs2REaexozpszC436dY+tMvKCpStOjTpKn8wfdqN8j69x8iXIorG2sLC9xNu8tf6ZTjQPABREf8genTpqPvgMGYPmlaZR9uctJNtLBsKWyLjWVra1yOVdyziL18BafPnoLPxK/Rhz85zl04q7IPNzUpBfa29sL2f6lMth07dkZiwlWhf9LFxQVubq5CvGv3rtBppot9h/YIExlrNdVXuj7bCrY2benWy3FzdcShY4HYuz8Q3bu7C5d25LO6Ojujma4R5k2bgMTkZBibmPOt4Cb0u8TF26MHIqIjEHIoCJfOn8fAoYOEz/p223ZwtnPGjFFTkJyaDJ3GuvQ7xOft9u0REXqM3w92I5n/fU+c/I2wBp5Ne1v+rwXGTZmADGkedHQMX/nhAxMTY7qlXDy9vREScgwnz4Rg97bdGDNhnHAs2PAnhmV844v04aZKpZCXFIv2WLBu1xZnTp1FRn4G/FcuxTdfTxX6aN+2tsZqv9X8MbIRGRlZKJOoPdeQ2MqsSfplY2Ov4VFpAd71rDl2bmC/QUi6lgI/v2UYNLBhDGp/mX7lVlZtUJrzCDl8BXqQ+XOrGTJqCN6x74bFc+fyO2IPGhUfCysLZKRnITGF/L7XVfZdEu96vIsPBn+MFT/9jF4De9Oo+LSyaIEH6kBRRg58Z/nWGMf9We/P0eeDvvjmu3Ho1dubRl8MaTG/6v2F140kjzfeeISoiGhs3bW1xn5AjJg8Hj/+8AMGDB9OI+JDTiwaGsAsn+mYNGlWjf2AGO0zA9MmT0Dvns/3wFeNhxrI8Kkt27dAoqYOezs7mPGXEnk5WTh35iz09AzQb3C/JypdGV27loiYC9EYPmr4C7fCyUGwZcsW0hGDDk4dhFEYeXl5OB1+GiVcCQb2GYi3bd6m7xYnUgd7d29HRmYGnNu6wcbRgt83HuD0qdPIzZJh0KABaOdgQ98tTqQOdu7cDWlGKro4dkFbO2s+9hDhZ0/gflo2Rowd8VL7AemO81u5DJ/2+kwpuw+qI3Wwe+dOlOTlouVbtnCwt0ERXwfJMTGIT0nFwEGD0L59O/pucSKNtnMR5xAefoK/4neFnV1bvl4eICYhCSkJiRg0tL8wauV5PPVx3YysTKQmJ/GVXAJ1LQ106NgRujrKn2Sr27btN1hb29QYRfAicvJykBCfgAL+MklfUxu29nai7aP8N6R/Nu1WKlLv3lHpOridchvp6WlQV9cUJvM2Nn75S/+Q0GCQIey9eynX4+//pXodSNS1YWNpheYWzUXbffA0JOn+lfw3/kxL4RucmsLDPi9aB6KePHzu3B/w9aQpwsQ1DFPfMtIzsS9oDyZ+PZlGGFUi6mRb8RTcP/taGIZh6pqoky3DMIyyUM4xXK8BGReobE++MeJHbjKFnw6nJUaVqUyyzc8tROCOQFpimNePnNz3bt8JTc1nP13EiJ/KJFsvL08kpSUJA/IZpi4kxCYguzAXXVzFPf8x83xUJtkSX4//GgG/7aIlhnm9gkMPYcKEr2iJUXUqd4Ps4cNSYeIahmGYuqRSLVuieqIV6zycTP3JyMigWwxTk8ol2+p2rtmKiGi2Pj9TO8hqC4cOHaIlhqlJpZPtkK9GIHDnJuRl1Jyjk2FeFGnRkkQ7fvx4GmGYmlQ62ZJJdUb7TMbaHQuQlcUSLvNySKLduH4zvv32WxphmCexJ8h4qamp0NbWENZYY5gXRfr+y0rlbA4O5j+xZMswL4k8Hfaqk4czqkOluxGeJiAgABEREbTEME8XGhaKkBDxLufO1D6WbP/B08sL4eGncSPpOo0wTBUyiXpA0C7ERkWj53PO0M8wBOtGeApyeei/+hcYNtLC2KmTaJRhgFnfTYdHD68nlk1imGdhyfY/SFOlwppcDFPhgVwOLTY/MvMSWLJlGIapA6zP9jn5L/cXboowqkOYizYsDD8tWEAjDPPyWMv2OZGVh4P+CEVqbDzGT/oaJsYm9BVGjJKSk7Bvzz44uzjg3Xc/YEO8mFfGku0LyszKRER4FD4b8CmNMGIUGRUBW1t79qACU2tYsn0FZCb+srxGkPDHY1N206RBI7/LwrwSNNPXVKklupm6w/psX0FZaQnGzRiOS1FRNMI0RGQV5mMHzmDcuNH8ybOERhmmdrGW7Ssiw8MOhhwUWkMjxoxgraIGhtwEW7tuNQyba6Fnj4EwNmbdBszrwZJtLbl27RrOXjgHnzFsir2GZE9AAFxcnGFjbUMjDPN6sGT7mpAWE8HuYisX8nspLCmEGRtNwtQx1mf7mpBJSpauWkJLjDIgUyHOnPktoiJO0wjD1B3Wsn1NysvLcSI8DFGnI2Bl2wF9evWEjo4WfZWpSzl5eQgJ3I209Cx49PBAVzd3+grD1B2WbF8zctl69Wo8NCXlcHTtQqNMXSKTwxfLitHGxpbNa8DUG5Zs6xhJvkGHgtDFzQ2tLFqw0Qu1jNTv+QvnEBN3ASOGfAkTE2P6CsPUL9ZnW8fIDTNLCwvMHT0avpN9aZSpDaRP1tf3W0SHR2LYqC9YomWUCmvZ1hOSGK7GxuHEiXDM+H4Ga+HWgs0bN6JDx46wd7Bj9ckoHZZslQh5ZDTkcDDcunjAwESbJYz/IJVKEXbsGHr36wNDfUMaZRjlxZKtkklJTsXhYwfwRoEcLdpZwPuDXtDR0aGvMpu3bUZGejqM9U3g3csbFuZscnemYWDJVoklp6ZW3kTLysriW3NpsGnXFjoaqpF8U9PSkJiUAFsbW1hZWQmxoiw5dIzZiAKm4WE3yJSYDZ9gKroSyGQpq1dvQu+PemO5/xKk8pfRYkU+24K5czF94jeIioiChP9TgSVapqFiLdsGpGIawMSrV5EiTcWgoYOEZEzi+TmFaKavjabqDevx4KKCUuQWZsPC3Bxqaopzf0BQAMxNzWBn1wH6urpCjGEaOpZsRWLHjl1IS0mFREMdZmYm6N69OywtLemryqXiia78kjI8KCqFmZUJBvXnTxxN2DwSjHixZCtCZFiZukS9sgtixYoVaMQ1gppEDXrNm8GtizusK/pAi4ogk8lhaKhb2bJ8UeTnyYpk4P8BGBsqRgZk5eQg+NAhlMiKUVxcjMelHMZPGs9GDjAqiyVbFRN7MRkWVtowNjYTygFBuxC4Kwj5+fnQ09ODlZUF5iyYX3kTLiw8DNn52cI2MajPILoF+K/2R1hoGPRkMsj47+3VqxeGDx8uvCbjY9IMKWys2NSFDEOwZKviHpaXo1z+EPLSMhSXlPBJsoxPuFXdD1HRkSguLBS2JXxr2cPDU9gmpOkZUNfUgGZTxU0rLXWtl24dM4zYsWTLMAxTB1gzhGEYpg6wZMswDFMHWLJlGIapA0/ts01MTBIeDZXJiiFRV4e9bUeYW5io1M2PpKQkpKenI68wC+rqGnDs4Kxyz+FnZeUhKTEBufn3hZtj9nYdYWGpGMWgKkgdJCRcRU5+JtTUteBgYwdrG8WwOVVB6iA5KREZ2VI0UW+KFkYt0dbOVqXW1yPzJMfz+0GmVApJUw2YGZm/cB00msuj28I/uMJvKYqLimFq2lIxKJ57AxHnjiH6Yhw6u7rSd4oXGXC/ao0/CnMfwMBQH2+/+TYaNWqE03+cwuGDwdAzaQYzkxb03eJE9oM1q/xx5ep1NDNshrY2b/Mn2kY4E30KB7YcgIGFnujrgIw/9vf35xseCWhmoAeHt+3RpLEEUTGR2LdzPx8zgHkLcZ94SksfYOWq9Yi5HA1tA13YtW3PJ1t1JN9Nw+F9QVBrrA7LVuJugJBj4WBIIA4eCIaJvhHeateOb3w1xp376TgQsB+aOpr8fmBO3/0MpGVbYfaMmdy8RfO5x48f04hCcfEjbsaMGdwX/Qdxf//9N42Kj+yRjJszcw43f+F8Gqki4+tk/qJF3KCBA7lbN/6iUXGaOWcON9t3Ji1VIfWzatU6btzo0VzCzXgaFR/yOefx+8D8hXO4R48e0agCOTbWLV3F9RvYj7tx4yaNig/5nPMXLeZmTJ1CIzXFx8VxI0aP4GJiLtGIOM1bNI/78ssvufPnL9BIlQuXLnADB/bh4uMTaOS/VfYLxF6MRZeurjDUMcaxE8doVGH//l3w9PTEhOnTsHfvXhoVn1vJt2BhYQEbSyuEh4fTqMKmtRuhX1yMZSt+RVhUII2KD5lpzMbGAta2Npg2bYLwdFiFkANHkJEhxXc//ICgPSE0Kj63pXdhrmsMG3NnkAs/MglQhR0bd0Can4Fff16BA4cP0qj4ZGZmQl9HDx3dO2PChNHIypLRVxQPrKzcugk//fAjggIP0aj4SFOlfGvWBHOXzMWhQ4E1joUMfh/YvXMLVqzYhr37d9Pof6tMtudjLsDerhNGjxiGi1FXhGRDJjiJiopGVk4WPDw84OTkhEePHghxMbp28Rq8e3uj94B+iIqOQlhYmBCPiLyIhw8LMHbBApiZGSMrrVS0dXAiJATubp7o128w7Pnf99Y1m4TPeiX6CuKSrmEBXwdW/AlJTa2cfof43LgcC/ceHhgwvBfsnW3h5/eLsFryxehYZMnuw3eWL8z4OigvKxEuM8Xo2LEw9PDyQE/v3nDq9A727FjDf1Y5biTdwNjhozBq0GihDgzMTURbB7HXYtG5U2eY6Zlh2KgxWLtqvXAsXIyN5U/CCzFsGF8HZtrQVtcW+rWfpbLPNiLqFP73YQ9I1BujUydHRF6OwdHg35Gdl4nJE6fgjTfeEL4hKek27Du0Q+NGjYWymBz94wi/g/0PEjUJOr/TGVfiLyNwx37kF9zDpElT0YjWQcpfqTA1MYGuCGekOnz0KPp+2hvq6mpwdHDG4zcaY9eW7fjz7p+Y8/1s+i7g3v27MG1hBs2mmjQiHsdOn8JH/LFAtLd1QDNDI2xeuR53M1IxYdJkaKorPvNff/4Nw+YGMNA3EMpicvx4GN778D3hszo7OqOxdmNsW7UBN/+8gR+X/oQ2dJKj7Jx7aKrZVJR1cO7MGXh/3FPYNub3ASNDfWzetB2Zt1Ph+/U8tH6zpfBa5p105D7IhbWVtVD+N5Ut20aoNiiBzL50r5hPOiReM6lq8kGxjkqQVPtcZBIXWRZ/+ahejsaN/3HHsYx/nzirgP+4VZfMhJqElMugLtEQWncVJBIJyuXirIRG/6gDeWkpyjXIvqCFxmpVx4Oc/0NGaYgS/3FJo6OCRNIUcv5qRl6uVmPy+saPG9XYL8RE9o/d+xHfgFfjK+aRGt/o0qlqzZfz1aTxHEvkV/5z5XKNyj6JnZs3IzVPiq+nTeETqzpOH/tdiBPZhXcrZ5MSGw3o0S0gYFsQkqXJ+HbWXGhrGCEyMpK+QurgHvQMq94rJrpaxpWXRKRfauPWrZjk84Mwm9fBkH1CnLh9+w6MjfVpSVw0+cvCimNBqIOdOzHpm6kw1GmO06dPC3EiNzsXBhratCQujZtyKC5Q9NOSPlr/ZSvx9Q+zYO/YVujDJStmEOl3M2FjLc7JhvQ0SfdAhrBN9of9O9dj1DffwOpNC8ybNQNFtC///v18/lh49nDAym6EvPwc5Ofl4naKFHfu3saMGd8LSdXOzg579gWhuZkxwEkQHRkN125dIaGX1GIiKytG4s2byC0tRHxiDKZ/NwNN+TOWrYMNDuwKQAFf4abNTREdfRGe771Pv0tcCmWF/KXhfeTl5mDJgl8w1ecrtGxjBhubtvjjSDik9/+CeUtrRIafhHv37vS7xKWsvAzXLibi4aMS7Fq1Gp8NHIE2rVrB0bk99gTsQW5hrjAsMvJkJD7o+SH9LnEh4+uTEm/iUbkMMyZ/h6+n+OBNi1awbPk2HpY/wIkzIWhn1wHhp/j9wN2dfpe4yMrKEBN9BfYd2mOD3wa81+MjvNW6Fdq1bY9SSHDi4D44dn4HoceC0ffTT559xU9HJQhDm+bMnM2tWuUnDH2prri4hJs/bz73hc9Y7taft2hUfMiAN/I5lyxcyMmKaw5/I3WydetWbvToEaIe/kbMmT2bW7RoPldYWkgjCmQ/2LtzJzfuy/Fc4q1EGhWnRUsWckuWLOLu38+lEQUyJGrv4cPckCEDRV8H8+cv4veFeU/sB8SFS1e5cePGiX7o15JlizgfHx/uzNkzNFLl5s0b3OghX3Bxcddp5L/VeIKM3FVc+ctKmJubwLGLM1oatUR2bjZCw44JfRKD+o0R/RpQZDD7+o0boaOlBTd3N7QwaIV72Xf4y8dwZGRkol+/fnB0dKTvFieyH2zcsgHynEdw8XBBhw72yL6XixOnw5CWmsrvB0Pg4KICdbB2JYrl5XBzdUUHO3vk5ucjLPwEpEkpGDhiiErsBzu3bELWgwfo4uICp45OyL2fi2vXYxGfkAjvHt5wFfmDTg/5Ogg5cwpxkVHo2rUrOnXsKOwHsVdi+ZZ/Inr09IKrixt993976uO64RERCF2/HYn5GWht0xqjvhgFZwdn+qpqiIqKQlDQbiSmJsLW6E30GTWZP+hs6auqITExlT/RBiI8LAItW7bE2LHD4ez8fDuWWGTwdRAYHixMkk7qgEyO7uamanUg4+tgPaLIRPF8Hbz74bv4oNv/RNtn/zRFRXnYHRiE0NBgmBqZ4pNPPkSnTu+9UB2w+WwZhmHqgEgHMDEMwygXlmwZhmFeO+D/AbcNKdwD6KlPAAAAAElFTkSuQmCC"></span></p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="qvB = \frac{{m{v^2}}}{R} \Rightarrow » R = \frac{{mv}}{{qB}}/\frac{{1.673 \times {{10}^{ - 27}} \times 2.16 \times {{10}^6}}}{{1.60 \times {{10}^{ - 19}} \times 0.042}}">
<mi>q</mi>
<mi>v</mi>
<mi>B</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mi>R</mi>
</mfrac>
<mo stretchy="false">⇒</mo>
<mrow>
<mo>»</mo>
</mrow>
<mi>R</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi>m</mi>
<mi>v</mi>
</mrow>
<mrow>
<mi>q</mi>
<mi>B</mi>
</mrow>
</mfrac>
<mrow>
<mo>/</mo>
</mrow>
<mfrac>
<mrow>
<mn>1.673</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>27</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>2.16</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>6</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.60</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>19</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>0.042</mn>
</mrow>
</mfrac>
</math></span> </span> <span style="background-color:#ffffff;">✔<br></span></p>
<p><span style="background-color:#ffffff;"><em>R</em> = 0.538 «m»✔<br></span></p>
<p><span style="background-color:#ffffff;"><em>R</em> = 0.54 «m» ✔<br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Examiners were requested to be lenient here and as a result most candidates scored both marks. Had we insisted on <em>e.g.</em> straight lines drawn with a ruler or a force arrow passing exactly through the centre of the circle very few marks would have been scored. For those who didn’t know which way the arrows were supposed to be the common guesses were to the left and up the page. Some candidates neglected to label the arrows.</p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Examiners were requested to be lenient here and as a result most candidates scored both marks. Had we insisted on <em>e.g.</em> straight lines drawn with a ruler or a force arrow passing exactly through the centre of the circle very few marks would have been scored. For those who didn’t know which way the arrows were supposed to be the common guesses were to the left and up the page. Some candidates neglected to label the arrows.</p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was generally well answered although usually to 3 sf. Common mistakes were to substitute 0.042 for F and 1 for q. Also some candidates tried to answer in terms of electric fields.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A proton is moving in a region of uniform magnetic field. The magnetic field is directed into the plane of the paper. The arrow shows the velocity of the proton at one instant and the dotted circle gives the path followed by the proton.</span></p>
<p><span style="background-color: #ffffff;"><img 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"></span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">The speed of the proton is 2.0 × 10<sup>6</sup> m s<sup>–1</sup> and the magnetic field strength <em>B</em> is 0.35 T.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Explain why the path of the proton is a circle.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the radius of the path is about 6 cm.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate the time for <strong>one</strong> complete revolution.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Explain why the kinetic energy of the proton is constant.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">magnetic force is to the left «at the instant shown»<br><em><strong>OR</strong></em><br>explains a rule to determine the direction of the magnetic force ✔</span></p>
<p><span style="background-color: #ffffff;">force is perpendicular to velocity/«direction of» motion<br><em><strong>OR</strong></em><br>force is constant in magnitude ✔</span></p>
<p><span style="background-color: #ffffff;">force is centripetal/towards the centre ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Accept reference to acceleration instead of force</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mi>v</mi><mi>B</mi><mo>=</mo><mfrac><mrow><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></mrow><mi>R</mi></mfrac></math><span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>27</mn></mrow></msup><mo>×</mo><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>0</mn><mo>.</mo><mn>35</mn></mrow></mfrac></math> <em><strong>OR</strong></em> 0.060 « m »</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Award MP2 for full replacement or correct answer to at least 2 significant figures</span></em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mi>R</mi></mrow><mi>v</mi></mfrac></math><span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>06</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>7</mn></mrow></msup></math> « s » ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Award <strong>[2]</strong> for bald correct answer</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><em><strong>ALTERNATIVE 1</strong></em><br>work done by force is change in kinetic energy ✔<br>work done is zero/force perpendicular to velocity ✔ <br></span></p>
<p><span style="background-color: #ffffff;"><em>NOTE: Award <strong>[2]</strong> for a reference to work done is zero hence E<sub>k</sub> remains constant</em><br></span></p>
<p> </p>
<p><span style="background-color: #ffffff;"><em><strong>ALTERNATIVE 2</strong></em><br>proton moves at constant speed ✔<br>kinetic energy depends on speed ✔<br></span></p>
<p><span style="background-color: #ffffff;"><em>NOTE: Accept mention of speed or velocity indistinctly in MP2</em><br></span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">An electron is placed at a distance of 0.40 m from a fixed point charge of –6.0 mC.</span></p>
<p style="text-align: center;"> </p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVsAAABACAYAAAC0qdQBAAALxElEQVR4Ae2d72sU+R3H5w/IEx8IDnhSWAM+CMgh8VEp6wNDi6AHh8jlwUIPITmkFCkGAtUex4VSBgI5FdvSBRVKpcc8MZSc6e0DRU7F5Uzxit0HDT1N56qeyLJi1HXzLp/Z+e5+Z3Zmf2R3Z/ay74EwszPf+f54zewr3/l8v5MY4EICJEACJNB3AkbfS2ABJEACJEACoGx5E5AACZBADAQo2xggswgSIAESoGx5D5AACZBADAR6JNsiCvYs0oYBQ37SM7iYd1CJbEARheV5ZEwvvTGGjGUj77yOPKPjA6UCcp9bWhkGzIwFu2m9Oi6FJ5AACfSLgGMjY6SQsR/2poSKg/xiHk60mHpTTkQuPZDta6zZJ2CmP0ZOZFlZQ252AoZ5AvZauDwrhSwmRLDzN92GV5xlzKZNmDM5FCMq2tHu0h1Ykl9mHssFL8dSActWBqZxCFb+eUfZMTEJkEACBHoq2xLyVhpGykK+nEBbgB4MkBVzmDFNTGQf1Huy7r6o30jrKGSPBhrt7TNnkSt2+2vnOfLWIRjpeeRLgbwq/4H94RiMiSwKgUPJ4GepJEACkQQoWz+act5CyjiKbGHdfyDy01PkZvbByNhwtDTh+TyEnUnBzPwWf5yZqIYo3B5xDvlb5+ohgvQsbNWDDZN/rZwKSoUVFIISrh3nBgmQQHwEXsPJ27AyY95320R65nI9nNgg2xbppeK1J9hqiLL6dLtW7dWqMKeRdp9uHXsKhvkeMpNe+W4nTMq4jJm0WfeNHuJ06yRhzwUtzQRm7AcotQDXZRihgmJuFqYxCcvO1gtvGrOtCjRctgJBr7KX1lCNKeJB9kOYblzYC1t4IQPVW61KO5hPCwo8TAIkEDOBCkr5eaSl85S9XxVV6T6yIl71VOqTbRvp1ZOrCmGq/Nwn5mIgjFCGK1vDRNq6g1LFwddfr6Go6lQLcd7EfEOdZFxKdfC8J+k2OpxdylZVWAafzuGOO8D1Gk7uY6QjC9+EbLXH/mq8Vw9R+GMxlG3M3xkWRwKbIuA94Wrfbcmm+v3eh5ncU8An29bpq+cGQpq1uvk9ASh36U/lrcuo1slfRqOTaoX6NnokW73CQuwBshMmUlYejbHoTchWDzm4F0DvufohVhuuH/e1lx9IgAQGgYDnCHf2Uu3xXs1O8jpTumzbSF/taOkdMb2hfk/UZTsF2/EsVc7DShmN3tJDk3qdVPZh+9QxbR0uW/dk1fCwdb1B1QZqFXYzrwo1fHaB12hdoACq+QSkjRAxu3XTZRqAqIPRGqo2y/lzmNJjMOoA1yRAAvER8OQZ7givGrrE2kjfN9m69fB6s3qdFK2wfeqYtg6XrZag5aYrt8B0KhdMyj9DoZZR2MwDr0vfMBthE7JFk9kI8B4TGsqpVY4bJEACsRBo47vok1jr9JsLI+gdxXbDCPXOpovKV89oeN3L1pObmbmIB+4ovxezVUHqkLKrUOqB8eh5tpuRrYxINptnO4HZ3Fp9mlpI/biLBEig3wTUgJeJ9Oxy9UWDioM78zIX3nvC9UmsjfTBATI159/Nr1QdEKt1tFTMVpetKmNMewcgbIAsMdlKjNZB/uKM9gaZGqmTC6YapT/6B944kxFBfcpH7TpvUrZyvrxBltXqZPANshpWbpDAQBAITrMKfEd9spUKt0gvSQJTv/S3WVWnznDfSlv1ZiPosg0rI/B2a0OdEBjIiwbbg55tdOY8QgIkQAIkUCVA2fJOIAESIIEYCFC2MUBmESRAAiRA2fIeIAESIIEYCFC2MUBmESRAAiRA2fIeIAESIIEYCAyMbJ89e4Zr167Btm335+bNm3j58mUMCFgECZDAViYgHhGfnD171v25evUqxDdxLwMhWxGsvCMtMJRsjx8/jvHxcRQKhbiZsDwSIIEtQuDRo0fYv38/tm/f7v3JxPqfHzh//nysrUxctpcuXYKIVaAEF/ltJBIOOxZMy88kQAIkoBMQb+zatatBsuqP34iA4xRuorKVrrw0vFmXXkILp06d0hlymwRIgARaEpicnIwUrRLujh07mvqnZSEdJEhUthIykNBBq0XCCezdtqLE4yRAAoqAdOBEpEqqzdbydB3Hkqhs5+bm3MB1q4ZKz1bBUmnVZ7WW/WpbrQc1bbN6BduxldKq66LWzdqm0qj1VkjbrA1yTLVV1mrR90XtH/S07bRBta0faYN5Bj9LGDOOpX5V4ygtUIb0aiVM0GoR2XKgrBUlHicBElAExBft9mxPnjypTuvrOlHZimild9tskWkb8puoWVy32fk8RgIkMHwE1HhQsBcb9lmmgsWxJCpbEWmr6V3S++UAWRy3Assgga1F4PTp077QTJhoZbZCXB25RGUrl1amd4lw792757vSImIRrRyLC4avAvxAAiTwgyYgDtm9e3ekcGXqVy6Xi62NictWWiqiPXLkiPsjYQXpyYpkZU3RxnYvsCAS2HIExB8yALZz586adE3TdF90uH37dqztHQjZqhZLUFt6uiJfSlZR4ZoESKBbAuIT5ZekBtsHSrbdAuX5JEACJDCoBAZOthLEbrbIbyj2epsR4jESGE4C7bihlV/6Sa652fpZckTeUTAEpBowCw6mRWTF3SRAAkNEQLwgYz3iiagOWZRf4sA08LLVJSuv98oIIxcSIAESCCMgfhBPREmXstWoKRiUrAaFmyRAAh0RiJKu8ktHmfUo8UD2bFW4gD3ZHl1lZkMCQ0ogKF3KVrsRBAZ/yID3AO+Bft0Dmm5i3RzInq0QkLlw6uUG9nBjvSdYGAn84AnoPVrxiJpbKwJPakmu5IgWB2FQuhGguJsESKCBQJRkVcKgX9T+ONYDL1sFQZcup34pKlyTAAkoAmrql96TVcfUmrJVJLw/oKx9bNiU/9gQNYeuITF3kAAJDA0B8UKr/+hC2Q7N7cCGkgAJDCuBgQsjDOuFYLtJgAS2NgHKdmtfX7aOBEhgQAhQtgNyIYajGq/gXD+P6QOjMIwRpA6cwGfX11Buq/ElfHPhGEbeXcDKW/2EbvLU8+E2CfSXAGXbX77MvUZgA+vf/AGHR/bi2Nxfcf2rZfzl00mMjryHhZViLVX4xluUVs7j8IgBI2UhX7NzN3mGl8S9JNAvApRtv8gy3wCB/+GLX+6FcfD3+OebjeqxN/dx4aCJbdOLeOztCpzkftwo3oZ18J3qm4U+2W4uz4315/jO+Q5PS8raFaw/fwzH+R6lcpOKhFWO+0igTQKUbZugmKxLAq9u4dMfGUhZeS1s8AIrCz+F8c5vcONFhOQ2nuDGmQPY9sFnuPTJT/w9207yfLKIqZE0fv2nc5geNz1xv4+5L/+Be5d/gXHpNUto4/DvkHNeddlYnk4CjQQo20Ym3NMPAo6NjJFCxn6o5V6GY0/BMKZgO6qXqR1GGU9yZzA++hGu/Psx8lbaL9tO8nTTGjBGf46Fpa+Qv7uEhWPV2PFoZgFLt+7i7t8XcGzbCPZad0Hd6teB270gQNn2giLzaE2gEzF6uW08XsLJPeOYtldRRqkHstVFqkR/CAsrJa/Eh7AzKRgZG07rFjEFCXREgLLtCBcTb5pAp7Itr8KeHsfotI1v3ThqL2Sr96yVbPVeNWW76evLE1sSoGxbImKCnhAo5jBjbsOPL9xHfebWOgrZozC2/QpfPKvvlfLerizg3cg/t7kHU4v/BTrJs0H2lG1PriszaZsAZds2KibsisDGKq58kPLPPNhYw+L0GIwjl7EaGB/beLqCv9m2+y9O5E9s2vafYWXGYJgZWJ9fxY3VF0AneVK2XV0+ntw9Acq2e4bMoS0Cb+AsnsToyM9wZulfePb8CQpLn+DAyD58tPgQrmtLK7hiWTiX+xaVhjxDwghoI0+VD2WrSHCdEAHKNiHwQ1ls+RFyc+8jVQsP7MHhuS/hqLmtrhCD08MUqTDZAmiVpzqdslUkuE6IAGWbEHgWSwIkMFwEKNvhut5sLQmQQEIEKNuEwLNYEiCB4SJA2Q7X9WZrSYAEEiJA2SYEnsWSAAkMF4H/AxbQYWDFs7s/AAAAAElFTkSuQmCC"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10<sup>8</sup> N C<sup>–1</sup>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate the magnitude of the initial acceleration of the electron.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Describe the subsequent motion of the electron.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mo>×</mo><mi>q</mi></mrow><msup><mi>r</mi><mn>2</mn></msup></mfrac></math> <span style="background-color: #ffffff;">✔</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mfrac><mrow><mn>8</mn><mo>.</mo><mn>99</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup><mo>×</mo><mn>6</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mrow><mn>0</mn><mo>.</mo><msup><mn>4</mn><mn>2</mn></msup></mrow></mfrac></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>37</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo> </mo><msup><mi mathvariant="normal">C</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>»</mo></math> </strong></em><strong><span style="background-color: #ffffff;">✔</span></strong></p>
<p><em>NOTE: <span style="background-color: #ffffff;">Ignore any negative sign.</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>q</mi><mo>×</mo><mi>E</mi><mo> </mo></math><em><strong> OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup><mo>×</mo><mn>3</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mo>=</mo><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo>»</mo></math> </strong></em><strong><span style="background-color: #ffffff;">✔</span></strong></p>
<p><strong><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>«</mo><mfrac><mrow><mn>5</mn><mo>.</mo><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup></mrow><mrow><mn>9</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>5</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mn>19</mn></msup><mo>«</mo><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></span></strong></p>
<p><em><span style="background-color: #ffffff;">NOTE: Ignore any negative sign. <br>Award <strong>[1]</strong> for a calculation leading to </span></em><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>«</mo><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>»</mo></math></span><em><span style="background-color: #ffffff;"><br>Award <strong>[2]</strong> for bald correct answer</span></em></p>
<p> </p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">the electron moves away from the point charge/to the right «along the line joining them» ✔<br>decreasing acceleration ✔<br>increasing speed ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow ECF from MP1 if a candidate mistakenly evaluates the force as attractive so concludes that the acceleration will increase</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>The cable consists of 32 copper wires each of length 35 km. Each wire has a resistance of 64 Ω. The resistivity of copper is 1.7 x 10<sup>–8</sup> Ω m.</p>
</div>
<div class="specification">
<p>A cable consisting of many copper wires is used to transfer electrical energy from a generator to an electrical load. The copper wires are protected by an insulator.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The copper wires and insulator are both exposed to an electric field. Discuss, with reference to charge carriers, why there is a significant electric current only in the copper wires.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the radius of each <strong>wire</strong>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>There is a current of 730 A in the cable. Show that the power loss in 1 m of the cable is about 30 W.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When the current is switched on in the cable the initial rate of rise of temperature of the cable is 35 mK s<sup>–1</sup>. The specific heat capacity of copper is 390 J kg<sup>–1</sup> K<sup>–1</sup>. Determine the mass of a length of one metre of the cable.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>when an electric field is applied to any material «using a cell etc» it acts to accelerate any free electrons</p>
<p>electrons are the charge carriers «in copper»</p>
<p><em>Accept “free/valence/delocalised electrons”.</em></p>
<p>metals/copper have many free electrons whereas insulators have few/no free electrons/charge carriers</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>area = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.7 \times {{10}^{ - 3}} \times 35 \times {{10}^3}}}{{64}}">
<mfrac>
<mrow>
<mn>1.7</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>×</mo>
<mn>35</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>64</mn>
</mrow>
</mfrac>
</math></span> «= 9.3 x 10<sup>–6</sup> m<sup>2</sup>»</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«resistance of cable = 2Ω»</p>
<p>power dissipated in cable = 730<sup>2</sup> x 2 «= 1.07 MW»</p>
<p>power loss per meter <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{1.07 \times {{10}^{ - 6}}}}{{35 \times {{10}^3}}}">
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.07</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>35</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> <em><strong>or</strong> </em>30.6 «W m<sup>–1</sup>»</p>
<p> </p>
<p><em>Allow <strong>[2]</strong> for a solution where the resistance per unit metre is calculated using resistivity and answer to (b)(i) (resistance per unit length of cable =5.7 x 10<sup>–5</sup> m)</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>30 = <em>m</em> x 390 x 3.5 x 10<sup>–2</sup></p>
<p>2.2 k«g»</p>
<p> </p>
<p><em>Correct answer only.</em></p>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>A power supply is connected to three resistors P, Q and R of fixed value and to an ideal voltmeter. A variable resistor S, formed from a solid cylinder of conducting putty, is also connected in the circuit. Conducting putty is a material that can be moulded so that the resistance of S can be changed by re-shaping it.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" 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"></p>
<p>The resistance values of P, Q and R are 40 Ω, 16 Ω and 60 Ω respectively. The emf of the power supply is 6.0 V and its internal resistance is negligible.</p>
</div>
<div class="specification">
<p>All the putty is reshaped into a solid cylinder that is four times longer than the original length.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the potential difference across P. </p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The voltmeter reads zero. Determine the resistance of S.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the resistance of this new cylinder when it has been reshaped.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, without calculation, the change in the total power dissipated in Q and the new cylinder after it has been reshaped.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>attempt to use potential divider equation or similar method ✓<br>«<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>0</mn><mo>×</mo><mfrac><mn>40</mn><mfenced><mrow><mn>40</mn><mo>+</mo><mn>60</mn></mrow></mfenced></mfrac></math>»= 2.4 «V» ✓</p>
<p><em><strong><br>ALTERNATIVE 2</strong></em></p>
<p>«current = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>6</mn><mrow><mn>60</mn><mo>+</mo><mn>40</mn></mrow></mfrac></math>» = 0.06 «A» ✓</p>
<p>40 x 0.06 = 2.4 «V» ✓</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>Pd across Q = 2.4 V so <em>I</em> = 0.15 « A » ✓</p>
<p>and pd across S is 6.0 – 2.4 = 3.6 « V » ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mfrac><mi>V</mi><mi>I</mi></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>.</mo><mn>6</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>15</mn></mrow></mfrac><mo>=</mo><mn>24</mn></math> «Ω» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>pd at PR junction = pd at QS junction ✓</p>
<p>so <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>S</mi><mi>Q</mi></mfrac><mo>=</mo><mfrac><mi>R</mi><mi>P</mi></mfrac></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mfrac><mrow><mn>16</mn><mo>×</mo><mn>60</mn></mrow><mn>40</mn></mfrac></math></strong></em>✓</p>
<p>24 «Ω» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 3</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mrow><mn>40</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>06</mn></mrow><mn>16</mn></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>15</mn></math> «A» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>0</mn><mo>=</mo><mfenced><mrow><mn>16</mn><mo>+</mo><mtext>S</mtext></mrow></mfenced><mfenced><mrow><mn>0</mn><mo>.</mo><mn>15</mn></mrow></mfenced></math> <em><strong>OR</strong> </em><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>4</mn><mo>=</mo><mfenced><mn>6</mn></mfenced><mfenced><mfrac><mn>16</mn><mrow><mi>S</mi><mo>+</mo><mn>16</mn></mrow></mfrac></mfenced></math> ✓</p>
<p><em>R </em>= 24 «Ω» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> for <strong>MP3</strong> from incorrect <strong>MP1 </strong>or <strong>MP2</strong>.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>recognition that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi>L</mi></math> leads to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi>R</mi></math> / «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>ρ</mi><mn>4</mn><mi>L</mi></mrow><mi>A</mi></mfrac></math>» = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi>R</mi></math> ✓</p>
<p>«because the volume of S is constant new area is» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>A</mi><mn>4</mn></mfrac></math>✓</p>
<p>16 x 24 = 384 «Ω» ✓</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«total» power has decreased ✓</p>
<p><br>Because current in the branch has decreased «and <em>P=I</em><sup>2</sup><em>R</em> »</p>
<p><em><strong>OR</strong></em></p>
<p>Because resistance has increased in branch «and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfrac><msup><mi>V</mi><mn>2</mn></msup><mi>R</mi></mfrac></math>» ✓</p>
<p> </p>
<p><em>Allow opposite argument as <strong>ECF</strong> from <strong>(c)(i)</strong> (if candidate deduces a lower resistance).</em></p>
<p><em>Allow “power doesn’t change” if candidate has no change of resistance from <strong>(b)</strong> to <strong>(c)(i)</strong>.</em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This was generally well done at the higher level. Some SL candidates struggled to calculate the correct current but earned the second marking point through ECF.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates struggled with this question. A very common mistake was to assume the current was the same in each branch, leading to a resistance of 84 Ohms. The placement of the voltmeter may have caused some confusion for candidates, and they may not have understood what the zero reading was indicating. It is important that candidates understand what voltmeters are actually reading and are familiar with different placements in circuits.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates recognized that increasing the length of the conductive putty would increase the resistance by a factor of four, but very few considered that if the volume of the putty remained constant that the cross-sectional surface area would decrease as well.</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This was an item that caused a bit of confusion for candidates. The prompt asks for a comparison of the power in the branch before and after changing the length of the conductive putty. Many candidates correctly identified that the power in Q would decrease, but either did not discuss the power in the whole branch or were not clear that the power in the putty would decrease as well.</p>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistance of R is 4.0 Ω.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>When S is open the reading on the voltmeter is 12 V. When S is closed the voltmeter reads 8.0 V.</p>
</div>
<div class="specification">
<p>Electricity can be generated using renewable resources.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the emf of the cell.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the internal resistance of the cell.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The voltmeter is used in another circuit that contains two secondary cells.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<p>Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.</p>
<p>Calculate the reading on the voltmeter.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why electricity is a secondary energy source.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Some fuel sources are renewable. Outline what is meant by renewable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.</p>
<p>The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m<sup>−2</sup>.</p>
<p>The overall efficiency of the re-charging process is 18 %.</p>
<p>Calculate the minimum time required to re-charge the cell fully.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why research into solar cell technology is important to society.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>« conservation of » charge ✓</p>
<p>« conservation of » energy ✓</p>
<p> </p>
<p><em>Allow <strong>[1]</strong> max if they explicitly refer to Kirchhoff’ laws linking them to the conservation laws incorrectly.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>12 V ✓</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>I</em> = 2.0 A <em><strong>OR</strong> </em>12 = <em>I</em> (<em>r</em> +4) <em><strong>OR</strong> </em>4 = <em>Ir <strong>OR</strong> </em>8 = 4<em>I</em> ✓</p>
<p>«Correct working to get » <em>r</em> = 2.0 «Ω» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> from <strong>(b)(i)</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Loop equation showing <em><strong>EITHER</strong> </em>correct voltages, i.e., 10 – 4 on one side or both emfs positive on different sides of the equation <em><strong>OR</strong> </em>correct resistances, i.e.<em> I</em> (1 + 2) ✓</p>
<p>10−4 = <em>I</em> (1 + 2) <em><strong>OR</strong> I</em> = 2.0 «A» seen✓</p>
<p><em>V</em> = 8.0 «V» ✓</p>
<p> </p>
<p><em>Allow any valid method</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>is generated from primary/other sources ✓</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«a fuel » that can be replenished/replaced within a reasonable time span</p>
<p><em><strong>OR</strong></em></p>
<p>«a fuel» that can be replaced faster than the rate at which it is consumed</p>
<p><em><strong>OR</strong></em></p>
<p>renewables are limitless/never run out</p>
<p><em><strong>OR</strong></em></p>
<p>«a fuel» produced from renewable sources</p>
<p><em><strong>OR</strong></em></p>
<p>gives an example of a renewable (biofuel, hydrogen, wood, wind, solar, tidal, hydro etc..) ✓</p>
<p> </p>
<p><em><strong>OWTTE</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE</strong> </em>1</p>
<p>«energy output of the panel =» <em>VIt <strong>OR</strong> </em>6 x 5 x 0.25 x 3600 <em><strong>OR</strong> </em>27000 «J» ✓</p>
<p>«available power =» 380 x 0.4 x 0.15 x 0.18 <em><strong>OR</strong> </em>4.1 «W» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>27000</mn><mrow><mn>4</mn><mo>.</mo><mn>1</mn></mrow></mfrac></math>=» 6600 «s» ✓</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>«energy needed from Sun =» <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>V</mi><mi>l</mi><mi>t</mi></mrow><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></mfrac></math> <em><strong>OR <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mo>×</mo><mn>5</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>×</mo><mn>3600</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>18</mn></mrow></mfrac></math> </strong><strong>OR</strong> </em>150000 «J» ✓</p>
<p>« incident power=» 380 x 0.4 x 0.15 <em><strong>OR</strong> </em>22.8 «W» ✓</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>150000</mn><mrow><mn>22</mn><mo>.</mo><mn>8</mn></mrow></mfrac></math>=» 6600 «s» ✓</p>
<p> </p>
<p><em>Allow <strong>ECF</strong> for <strong>MP3</strong></em></p>
<p><em>Accept final answer in minutes (110) or hours (1.8).</em></p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>coherent reason ✓</p>
<p><em>e.g.</em>, to improve efficiency, is non-polluting, is renewable, does not produce greenhouse gases, reduce use of fossil fuels</p>
<p> </p>
<p><em>Do <strong>not</strong> allow economic reasons</em></p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>a) Most just stated Kirchhoff's laws rather than the underlying laws of conservation of energy and charge, basically describing the equations from the data booklet. When it came to guesses, energy and momentum were often the two, although even a baryon and lepton number conservation was found. It cannot be emphasised enough the importance of correctly identifying the command verb used to introduce the question. In this case, identify, with the specific reference to conservation laws, seem to have been explicit tips not picked up by some candidates.</p>
<p>bi) This was probably the easiest question on the paper and almost everybody got it right. 12V. Some calculations were seen, though, that contradict the command verb used. State a value somehow implies that the value is right in front to be read or interpreted suitably.</p>
<p>bii) In the end a lot of the answers here were correct. Some obtained 2 ohms and were able to provide an explanation that worked. A very few negative answers were found, suggesting that some candidates work mechanically without properly reflecting in the nature of the value obtained.</p>
<p>ci) A lot of candidates figured out they had to do some sort of loop here but most had large currents in the voltmeter. Currents of 2 A and 10 A simultaneously were common. Some very good and concise work was seen though, leading to correct steps to show a reading of 8V.</p>
<p>cii) This question was cancelled due to an internal reference error. The paper total was adjusted in grade award. This is corrected for publication and future teaching use.</p>
<p>di) The vast majority of candidates could explain why electricity was a secondary energy source.</p>
<p>dii) An ideal answer was that renewable fuels can be replenished faster than they are consumed. However, many imaginative alternatives were accepted.</p>
<p>ei) This question was often very difficult to mark. Working was often scattered all over the answer box. Full marks were not that common, most candidates achieved partial marks. The commonest problem was determining the energy required to charge the battery. It was also common to see a final calculation involving a power divided by a power to calculate the time.</p>
<p>eii) Almost everybody could give a valid reason why research into solar cells was important. Most answers stated that solar is renewable. There were very few that didn't get a mark due to discussing economic reasons.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.</p>
<p style="text-align: center;"><img 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Q8++MBlm017m2OUyJGDlEj41yd1pfpXfbvMWt764E6Rz1HkY4PObClaK23tFPnzEydOWCej604IFBUVoampCQaDQfirq6vDqlWrOsnhn4/4wuecTVpaGnWx+tEr8K9+ZCuZ6iIC0hxFLl4+R9FFxeGRRx7p4AjDw8NdVZxPym1oaOhgF//BYetHR4eEPbwhdVP2MHufZuMOkv9NmzaNeif6tCbcUzg5Rvdw9tlSJKfI5yja21bK2cbzlg3f51E6Bg0ahIULF0qX9OkAgYiIiA6pMjMzsWLFig73/emGPefdv39/DB06lMYc/eRloDFGP6loV5jZ0zmKztCFR6MeO3YM99xzj7AIOY9gpcNxArzuZs6ciS+//FLI9MADD6C8vJzGGK3WdCWH6Pg75UspyTH6Um260RbJKfIVbaZMmeLGkqkoZxKQ5u1FRUU5U2wHWd4WfEMOsUMV+tUN6kr1q+p2jrF8juJjjz2GDz/80KX7KDpHW5LSGQFXO8TOyvbUZzExMdRl6qmV4ya9yDG6CbSvFCMt1VZTUwP6UvWVWvUMO9577z1hpaO+fK/ovfaMd6GvtaCu1L6uAS8q3x1zFL0IB6nqZAK8u5X/8QUb+EbWfekgnWwaifMyAuQYvazC+kpdaY4i31zYlXMU+8q+viiXBxD95S9/ESbZjxw50u+7peURoeQg++KNpDIlAjTBXyJBnzYJ8OkY2dnZwsR9PkeRnKJNTN2+yZ3i2LFj8dJLLyE3NxezZ88G70r01UPu9Byxkc8Z3LNnj7A6z4IFC4Tl/xzJ51VpWquQEx6OFLUWRgBGnRopgaOQU/WVG8wwwqCrxIa83dDxwt1evoMmGrSoyEkRehICA2dBrfvOwYy9S0aOsXf8fDq3NEcxKCjILRP3fRqmlXG8pchXnpEO7gi4k6TDkoC1g+TR0L56KKIycFBfjbUJA91g4teoUb+OlZ+071jj3vIdMfE76Pa+gfTdkSituwW9fg8yovo7krHXaSj4ptcIfVdASEiIEJ3X3S2jfJeI8yyT1ii1ltjdlpV1fk++7o1tkoPkqx7RmrieXMuu0E2JoH9zs6tidBABOwSUSqWdJ3S7twTOnTvHfvrTnzLOWPpLT0/vrViPze/IuyRxsP4cMmQIe+ONN9jt27c91r6uFfueXT9bzgrTYk31rUpjhX8qZGkqFUsuqWdtjLE2bQlLVsazbM0tfsX0mlymUiaz7N+vZWkq/p5Iz7isnSw7USW+O8ksu0TDtHe4lPaj7foZVpqdLKaJZWmFh8Q0t5gmO9783klyLcvnctrYHa2GlZhlqFhidgnTaPViIZKOqez3mr/aKatdnw5nd7RMU5LNEqX/A4nZrESjZXeEoutZSbJkn+n/iCpbw6SSO8hy8g3qSnXFDxySSQS6IMCDbQoLCzFwoKnbbMaMGVi5cmUXufzrMW9h8mXqzp8/LyxVN2DAAC8FYIShdhvmJr6Lr6buQSNfd/XSMgw7dxQVLV2ZdBK7T4Rg2aVmNNfvxnPxAWisWILRM44gZM1pNHNZjYWIOp6FyVkH0CiNFzZW4PnRM/EeFqCmsRn6xjKM/2ypmGYgEtZ+iPcXRgNji1DTbKv71giDdicWT87C8ZDXUd+sh775NNaEHEd6/FxsqJUr/hGWFFRCmbFHWE+2uX4Dwg6+hIXvnIXBnnmGz6BenIr04yqsqefdpLdQv0aF4+mTMXVDNQyKaGQc1KKmKBkIWoz3rzbjytoEKO3Jc/Z9JztaEudDBBz5le9D5pIpfUxAain6RgtRDtPUQuvQ4tFrWHaXLUaplSjKs8pjLkW4L6X9lmlLUplSlcs0eqkV2d66K9F+yxgTW43JJUwrJrFsMYo6zy9n1yQRQmHyfJJMqVxJG3ka6Z78U8ynWszKr30veyDJS2UmHW3ZIUvuwlNqMTr7lwbJIwJEoMcEfKOFaGV+60Uc2n0TMVGDESB/FDAYUTHdCSYxorX2CHa3DEJsxL2w+PIWZN3E7kMX0Wq8ghP7TgMxwxAWIKVSQJmwClccDWCRdB4Tg1BJhKB7AMKiIoC6L9BoEJuncpscSvM1ag8dRkvMLzE8tJ8stwIBYcMQgwboGu22NWXpXXfq5hFN1xlCkokAEfBcArxblAfQdHZ09byzvJ78zHijARfkPY+9VlaL4mnDUGxDTlCsjZs9uNWlzi2X0XDjLuJ6IBvG22i4cLOTnDdxoeE2jAkWPyM6Se/8R+QYnc+UJBIBIkAEzAQUIRGIDQIumO/09iQZRTU77E9dMGp7WwC61DkoEhEh/YDGHhSluBcRsYM6AWKjRdyDYnqTxaKR3BtBfZGXT5LOz8/HkiVL+qJ4KpMIEAEi0DUB5QgkzR6EOt11y2AUw3Xo6rozYV0BZdwkzA7S4tSlm8KiAObCDdXYMDHatFiAIhyPzBzdobvTtIBA+4IC5ry2TiSdT9WhyaLH1IBGXYNVN60tAZ3dG4C4pMkIqjuHS013ZQmNMDR+gTpEICqs71qLXCGvdIySQ+SRfZs2bYKt3chltOmUCBABItCHBAZiwkvLMGV3Fl5Wf2ZyjnxFl9XrUdzdLlblOLy06VFUZuZjS3WTyTlyWQX5WImFKEh9AAr0R2TKc1gcuR8F6zQmx2ZsxLEd+3DyoSwxjThWKFD5DgbDP634DED8My8ioXIF8rZ8LDrHVmjVy5BeHILlBTMQ1WPvoYAyfjbyE/6GzLztqBacoykK9uX0MkQuX4JUN03ktzLafNlj08wS3Hhi7RB9dUzCjUipKCLgFgL+/n9VETYVRYfX4+fH5yKML5YelokzD6Vj+djuBN/wquqHsOmrcLh0PG4sG41gQdYsHBi4AJqyRYgTg20UoZOwsmwnnm7biAeDAxEYPBYFbXNkaUTneXcF4oOjMXPvF5YtUCgQED0PWw8XYfyNApOMwBFYpBuD0poyvBYX1Lv3JuDnyNi6F6Xjv8SyB3+CwMBghC36b4wvPYwDr42yDFLqXUk9yu0Vi4hzh8jX6fzDH/5gcwB/4sSJwu7jPSJAmewScCRgwm5mekAEPIzA3LlzBY34Qvi0c4eHVY6HqePxjrE3y0h5GGuH1fGUX9fkGB2uMkrYBQFPeJf4IgpHjx4VFqQeP348yEF2UWl+/Njjo1IrKyuF1S8aGxttthZ53VGL0Y/fYDLdJgG+APyiRYvMPSlvvvkmXnnlFZtp/e0m/+H55z//GcePHwc5SH+rfcfs9fgxxocffhinTp3Cjh07EBMTI/zac8w0SkUE/JfA2rVrzU6RU1i/fr2w96P/EuloueQgJ02aBN7NqtPpOiaiO35JwOO7Uq1rpaqqSti/Tt6CpBajNSXnXHtC95dzLPE/Kf44BOGMWp4/fz42btzoDFEkw4sJeHxXqjXbhIQEoQUpOcj/+Z//sU5C10TA7wn84he/wKeffmrBYenSpcjLy7O4508X0hijLZv5D4mhQ4di3rx5th7TPT8j4HWOUaofuYO8evWqdJs+iQARAMDHFHn3oMFgWnOS7+KRlpZGbKwISA5x1apVGDdunNVTuvRXAl7rGKUK4w6SDiJABCwJ8P8XvFfl8OHD+OEPfwjeWurLbZs8rVueHKLl+0JXlgS83jFamkNXRIAISAT4XD2aryfRMH32798fP/vZz0AtREsudGVJwOOjUi3VpSsiQASIQM8ILFiwQIjU/etf/+q8blOjFuqUcITnVKG1Z2pRLqcTMMKgq8SGvN3QWazz6nhB5BgdZ0Up+5AAn5fHF4vnXWCPPvqo0E3Yh+pQ0V5IIDk52XkOUbJf2Gn+int3l5fKpk87BL5Gjfp1rPzkWzvPu75NjrFrRpTCAwjwyenbt28XNOHRljyw5Pz58x6gGangCAFPWc3JEV0pDREgx0jvgFcQ2LNnj4WePNry448/trhHF0TA7QRsdqW2QlelRs7EcKGHIzAwBTnqKujMO95/haqcUQhM2Yaq6rL2dOHp2HBEZ7k1lYVBUr51qKjchPTwQJP8iTnYUduIVt59mD7SdC88HZuk3TcEGbx7sQrqnBRRp3BMzFGjSid2AAt2iNtW2Sizvav4LppqZTrbta0nOgLGpmrssKcjjGitykN44CxsrzomSzcS6RsqRb6c0WOYVqwFTmYhPngUcqq+srDIkQtyjI5QojQeSYBHW3rrwRfG5yut8E86fIkA35ppCSanH0fImtNo1uvRXP86Qo5nIX7qFtSanSOAk+tQUH4PMg40QK+/hfrSoTj476/hndou9qI6uQ1bNeHIvdQMfXMd3h99AS8nxmDE6ssYv6Yaev1VVOf/HxTNXI0DjXy/Q9OWTosnZ+F4yOuob9ZD33waa0KOIz1+Ljbw8oQ9HEfi5L6PcVk+Ltd6EYd2A7OTRkCJu2isWILRM46YbdM3FiLqeBYmZx1Aozxft3UEjI0VeH70AlRJOuovYlvUKaRPzkOFYIf0nnyEJQWVUGbsEZYJba7fgLCDL2HhO2dhwEAkrP0Q7y+MBsYWoaa5GmsTBkoZHf9kdBABOwSUSqWdJ+6/vW3bNjZ48GDGdeJ/Q4cOZbdv33a/Ik4ocdOmTez+++8326LRaJwg1bNFeNK75FRSbfWsJFnFVNkapueC9RqWrYpl88v/ztrkBQn3VSy5pJ61sVtMkx3PlKpcptHLUlmkkWeWzm3la2N6TS5TKVNZifZbKSFr05awZGU8y9bcYkwsTzW/nF2TFSfdVyaXMG0bE/M8wQrPNotyRNmSnvb0E+5blmVpm+M6SrqYDZF0F/hKcqSypFQiF9EOa7ukVN359IAWY3vzWK3ju1l/B516FgLD81DVKv8J4riz71ZKgw5HNqzGDqFsntPN5TukLO8GqWjvcklR9zjayqHiPDDRwoULUVZWhlmzZoGv4HLs2LE+nZfXU0TXrl0TlhyTtxSnTZtGLceeAvWofEa01h7B7pZojBk+yHIX+IDBiIoB6nTX7XeVOpKmJ/YKrb6biBkTg1CLb3xxs+K6L9BoMEIRORELUr/EW/vOmSJsjVdx9I+HEfnSVMQrIdo2CLER99qw7SZ2H7rY88hcQUctgmIjEGJDx5bdR1Br1x9Y2tETRNZ5PHAeY39E8SZyhrWqrrg2orVmB55deRn5T0ry3Vm+VGYXn8bPsfeVTOweugl1h6cjzOLF6SKvDz3mk9a9fUGHuro6m7vEfPXVV17p6H3o9XKCKXdxo+EyOusIbbnQgBvGEb0rK2YYwsQNiR0RZLzRgAudKnUZDTfuIiFqCCb++nEg/Qhqcydgwo2jeHdvBObU/ELYONg0GqlF8bRhKLZRcFCs7GY3dZRythRPwxCbwhdLSdzy6YGO0S12e2ch9wbh3/zUKXpnhXXUWtohRh6lyVek4Uu20eHtBPohJCISQbhs1xCpRdRoN4XzHyhCIhAbBFywJzooEhEh/QAooIybhNnIxqHaFxDWcAgnxyZhc2R/YZzSlD0ZRTU7kBHF79k6uh/o0i4lCGOLKvFBRrRli9ScwNjzFqlZhmMn7v+aNTahtmKDOaIqPP0/cLBW/ppYdWW2ViEnnEdQbTFHXJkjpLisHTmYGNgenaWuso7qsoqiMkd+8S7c5RgxbSta8BGy4geJk3Styhc4uirKjAvvPFrMqFMjJXgUsk62QPg1FdizKCvHXgdK5WoC9913H55//nkhMpCXxedlZmZm+nxrUf5DwNWM+06+6FiCtDh16SYsBoIM16GrA2KiBgutL7fqqByBpNmDUHeqDk2WSqFR1wDIW3dCWmD3B39Exb7zGDtzHCIFL9GZbdXYMNFWRGs3rLSrYwtqNzyJQDcPH7nZMbag9j+eR+LWZkw9fBV6fTMu5Q7DuYNVnXY/AC04u/siBiw7Dn3z5zj8XByUxiuoeD4FM6pUWFN/S5DVuO1nOJ6eiqyKK+JLKUZRJe4CFleiUd+MxsoEfPYsT3MVAQkrcfH9xQgC/xV0084kXVdGmXUdLaaIysDB5moUjQ1C0ML3cVXfwyirbryjlNS1BPgOFydPnkRNTeTlVcUAABC8SURBVI3wSRsIu5a3W6Ur4/BMfjwqM/OxRZouYfgM6pezUByZhYLUB+y0hlyp5QDEP/MiEipXIG/Lx6Jz5N9ry5BeHILlBTMQZfYEAxA/89eI/P1qrD45EjMfCW/XVzkOL2161Mo2LSoK8rESC3tp20BMeGkZpljpqKsoxNKVsNKxK1bimKOQ7DsYDP/sKkOH52YcHZ644kbrOex76wYWvp6F6VFKoekeEDUVua/PRVAX5QXN/jWeilYCip8ialgAWo+9i8y90cjPzcCoUFM3QED0PGwpfRyVme/iGB+oNTbg0Lv/BSxcitzp0QiAAgHRjyNtdj/sffeoZViyvfJba/GHFTWYsmkFXh4VKrwkitBxyNxShIWXi/D63s/bfxkGzcXruVMRJfT/90No3KOID7qAoxesfj2ay/oaNX94G1VT8rHq5XGmgXFFKEZlbkDpwhtY+Xq53wXZmNH4+AlvOfJ1TPmnPxy8ZewfhxLRGRtxuHQ8biwbjWDemxX2G+jGF6HmwMuI68bYoPN48e+9edh6uAjjbxTgwWDewzYCi3RjUFpThtfi5N++CgT8MgVz+A/x1F8hSehGlTTph7Dpq6xsm4UDAxdAU7ao17YpwqaiyELHIZh8IBiLNb/DqxY6SvrY++yPyJTnsPjuCsQHR2Pm3i/av6PtZbG+350Q1t6llUJtLcOKuUxTaLF0/1umLUltD2UWQoGV7eHQghK2wpZN2snDlE3nUoi0Le1t6SQv///ZDIUWJFmEadvRxyKNjfLthT8zuQ48jtoqJNyGKFfc4iH2V69edYVokulnBHx2uoaf1aO/mOvGFmPXEVvWTrvL65atmDYkWFzJwTTOGByfhZNdZnQ0Qdc6m6LMHJVnmc7RaDHLXO67+vDDD/HUU0/RCjPuQ04lEQEi4AEE3OgYpYgtJ1otrGygF8Lf+eB++5+zxuG61lmKMuuJVVK0mN285mgxuylc+oBv3PrOO+8Ii3fT8msuRU3CiQAR8CACbnSMUlRTA3SNpl3FTRyMMDR+gbpuQRmAuKTJCKo7h0tNfMkj6TDCULsJEwNngS8WoIgch5ljrSfVilGnYhopp+1PSWcXRZnZjcQydIwWs62gy++OHDkS+/fvF5zje++95/LyqADfJOBJUal8kQU6iEBnBNzoGAEIUU0PY3f6Mqi1fLoon6pwAKsLyrqISrU2QQHlhAXYNOVvyMzbjmrBOZpkFSwtBpYvQSqfZ6OIQMrSZxFZvB7rqhqFAVhj0wns2HUeDwlpfoyAsGGIEcQb8Y3hm46DtC6NMutOtJg1A/dd8wAR7hzff/99vP322+4rmEoiAk4mwNenHT58uLA7Cz+ngwjYIuBexwgxqqlkOI5PGYLAwGCELTyLhxYvwlhb2nV2TxGO6UV7UTr+Syx78CcmWZMPYODiP6Ls1VHiXKF+CE3IQZlmDtoKxgoRYsEPbkTb0zvNaRSRSVi6uBVZ8aEInfknG5Gqrowy6060WGcwXP+MO8ddu3bhwoULWLNmDfj+iHR4FwE+PaSysrJPlp/zpKhUvsjCn//8Z0yaNIkcpHe9wm7T9gc8yshtpVFBXk+AO8Tf/va3aG5uxubNm/GjH/3I623yBwOSkpJw+vRps6n5+fl49dVXzdeuPuGO0RO6U3krMS0tDXxpPunguo0fPx5vvPGGMIVGuk+f/kvAzS1G/wXtK5ZzR7hu3TrExsaCT0yn8RrPr1keQCV3ilzjN9980/MVd5OG3GFTC9JNsL2kGGoxeklFeaKaPBhn27Ztwvijv0xU98R66EqnnJwcFBfbWpm5q5z++5xPVeJR2XT4JwFaRNw/690pVj/99NMYNmyYMNeRt0p4BCsdnkfg/vvv76DUD37wA7S0dLblQocsPnHDVleqZFj//v0xdOhQrF69mpyiBMVPP6kr1U8r3llm81/VGzduxIQJE2ghAGdBdbKcF154AdbOkY+n0WEiwB0iD8j505/+hFOnTnn91mZUr70nQC3G3jP0ewncOV66dEloOfKxqylTpvg9E08DwKOJeUQqP3grn/+58/CU4Bu5zfIWorfv8ym3i857T4DGGHvPkCSIBHggDl9Cbt68eXjxxReJCxEwE/AUx8i7UuPj44UWIu8yJYdoriI6kREgxyiDQae9J8Cnc/BoVR61mpGRQdM5eo/UJyR4imPk7+fVq1dpWoZPvFWuM4LGGB1i2wpdRZ64IXI4UtR1aNVVYkPe7j7cFqoVuiNbkLdDK67WY2uDZYeMc2oiPp2Dz2/kXXfcQdJCAE7FS8J6SYC/n3y7LzqIQGcEyDF2Rkd8ZtTtxyvpH2Bo6ado1l/BwYyfolb9OlZ+0oerv7TWQv3sRnzSJhnQH1EZe6C/sgoJyr6tVv7l8+6775rnOn799deSkvTppwQ8YXK/n6Ins3tAoG+/QXugcN9l6Yd7g+5p38267xTxmpL5OCPvUn3sscdoIQCvqTVSlAgQAdjcePKOlmlKslmiUsn4BqNKZTLLLtEw7Z02vq2wefPe32sOs6K02PY0pWfYdZ5EOtqus7PlhSxNJclRscTsEqbR6qUUwmfb9TOsNDtZlBPL0goPiWWJybicUpk+idmsRKNldyykfM+un93JshNVJjmqNFZ4WEojbiScmM1+X5jGVNwmVS7T6PkmwJ3pKG4YbObA881g6XNGiLpyu+JZtuaWhSamC7HM5LWs/FBRO4PEbFZ69hrTaw+xQomdKo0VnbnO2tG1sTtaDSsxM7HiJm7ebKobyZZ/WG7wLCihZ1pNSTsTi3rkCSQd32aaM/bY2TCtm7dOnDjBHn74Ydr0uJvc/DX58uXL2XPPPce0Wq2/IiC7+5iADcfYzM4WPsFUaaWsXnCE3HccZrmJUSy5pJ61mR0j/0KWvtD5F3k5y06MYomFZ0SHJcl5m525/r3JzLZrTJObzJSJReysJPtaOZuv4l/85SZneOciK0mLZar55eya4If/zsrnxzJVmiSnjd2pL2Vpqlg2v/zvojP5nl0rX8xU/Iu/vJ7dYdZpRAegjGVpJRfZHfY9u679O7vDHNRRW8KSLRyg5FBKmLbdm1lVpVSmzDbJfqVSZo+e1ZfMZyrVYlZ+jXNq1z2t6ITph0bbdXamiDv0J1jh2WZTOYJzVIl1wm+JTlxy+EySK9URr8cTph8yZv42dORsNCtYorwsK8t6csmdI3fk/JMO/yPA697RgztFnn7IkCHkIB2FRumcSqCjY2yrZyXJkhO0VZbUYpQ7Jp5OvC99MQtf3B1bU22Ck0llJdpvbXyZy+QoeZp/mFunpvSSPlZlCTqrmCpbw9rbonLnJZ5LukliHNKRMZPOclvksiVh1p+2ypTYSfab8ljKN+Uz/zAwi7UqsyvHKDy3riPGmEU+WzpapzEr0OsT3gLgLUdyjiaU33zzDXv11VcFJ/DII48wjUbTa8aeKqAnjpHnIQfpqTXq23p1HGNUDELsxGicXPEHHKiuQkWVDvJthdt7n6MxZvgg2ZibwrS3YcthHKr9GlAmYO2VaqyN/xpVFRWo4H/qHEyOz8JJSYjxCk7sOw3EDENYgKSKAsqEVbii34OMqG9Qe+gwWjrsZG9ZlvHyx9h3EoiJGixuN8ULGIiEtdXQH8xAlCRaKlf6dERHKa27Plsv4tDum4gZE4NQC70DEBYVAdR9gUaDsQttjGitPYLdLdZ1BCBgMKJirDdvthLnSBqrLI5c8mhAadNj2tcRWLRoEbZv3y6g+/TTT2kLJDsvEQ/c2bNnj7BN1IIFC0D7KNoBRbedRsDGyjdBiHutDDVxR3GifD2yirkbC8JDC/PxesZTSIgK6KLwm7jQcBvGhH74XL0EU7L2ouWhhSha/DCCg1OwTROJzMR3oWs0AJFdiJIet2zFtCFbpSvZZzRiZVfdP22Ftisd+YbHvTksnH7Xgow3GnChsyUsWy6j4cZdJIR0JusubjRc7nTz55YLDbhhHNGZEJc844uN8wWa+cLW3Dn680IA5eXlFowNBoMw+dzipg9d8LmMvTkkB8md5Ny5c2nT7N7ApLydErDhGHl6JaISpgt/GWvvoqn2A+x6awWmTf4C719cgbhORQ5CbMS9gG4/MrNqMKX0U/xuerjYsjSitaoSfCe0bjm0sUWo+cB+y8/Yw424+TQMp+nYKRPHHypCIhAbBFywl6VD69lWwn4IiYhEEC7beijcC4qNQIgCaLSbwnUPBgwYIMx15PMceQuA9nVsZ83XnZ0/f377DT884+8Ed362Du5cf/zjHwv7J9p6TveIgDMIWHTW2RbYD6FxU7Eg7XEEia0VU7oGU6vPnMkIQ+MXqAuajKS4INM5rLvy/ok7La3mHFCE45GZozt0Dxp1aqQE8on0/4tfJk1GUN05XGq6254PRhhqN2Fi4Cyodd9BETkOM8dadw+KE97FNLLM4qmob1c6dszo2jvKEUiaPQh1p+rQZNFjakCjrsGq29meKgoo4yZhdpAWpy7dFBcAENMarkNXZ93tbE+O6+5LCwFI+zr640IAfF3ZgID2HpiBAwdixowZroPuxZK5QwwNDUVhYSHOnTuHWbNmebE1pLqnE+joGI1aqFOiMTGnAjppLMvwOY4e+gRI/RWSIqWuRS2KC4pQoeOOzgiDdideTv8AUzYtwATlv4pfzKexa8cJ8Qv+LpqqtyMv8z1ZF19/RKY8h8WR+1GwTmNKZ2zEsR37cPKhLBSkPoigCQuwacrfkJm3HdWCczTCoDuAgqXFwPIlSOVdnYoIpCx9FpHF67GuqlFwBMamE9ix6zwektJ0qAnJeXSlY4eMfKDONN4nPPoOBsM/bSXq4b0BiH/mRSRUrkDelo9FdrzLdxnSi0OwvGCGacxUGAcU6+IbA6SqMheqjMMz+fGozMzHluomk3M0fAb1y1kojuRsH5CND5tzufWEO0dpruOcOXP8bq4jbzGXlZUJX/JLly7FsWPHwFvTvnj0tBvVlkPk7w0dRMCVBDp2pSqika7+I4J3vYXJYemiE4vA9OX5KH/lcYQpAFObbywWzvkZvlg9HoEVDUDQdCwv2YsXJondpspxeKV8FTYvfRYPBvNBMy5jGdL2lSBk5nqzTYrQSVhZthM7N+fjweB/F8czV0FTloo4ISAnHNOL9iJorxrLHvwJzvKcvKxNf0TZ1Dgx2KYfQhNyUKbZi81LxyJ4Gi9vLBZu2YmyeaMQgK/M5VmcOKijRR7hQnTou55FfPAKjC2qxAcZ0U5yNAoERM/D1sMq7FUX4MHg9jHe0ho+xqs0qSP8GJiDXdNGITgrGUU1v8MjFooqEZ2xEYcj9kO9bDSCz4pMiopQkzoBUeZgJ4tMfXLBnePgwYMxfPjwPinfUwpdv779/4Wn6NRXevCdL4KDg7FixQo8+eSTtOZuX1WEn5bbg0XE+TjhcoyYdhn5NTuQ0dvgFD8FT2Z3JMB357j33nvpS7AjGr+6I40vkkP0q2r3KGM7thg9Sj1Sxp8I8IhVOogAjR/SO9DXBDqOMfa1RlQ+ESACRIAIEIE+JNCDrtQ+1JaKJgJEgAgQASLgYgLUYnQxYBJPBIgAESAC3kWAHKN31RdpSwSIABEgAi4mQI7RxYBJPBEgAkSACHgXAXKM3lVfpC0RIAJEgAi4mAA5RhcDJvFEgAgQASLgXQTIMXpXfZG2RIAIEAEi4GIC5BhdDJjEEwEiQASIgHcRIMfoXfVF2hIBIkAEiICLCfx/EMj4cjdfQHwAAAAASUVORK5CYII="></p>
<p>The mass of ions ejected each second is 6.6 × 10<sup>–6 </sup>kg and the speed of each ion is 5.2 × 10<sup>4</sup> m s<sup>–1</sup>. The initial total mass of the spacecraft and its fuel is 740 kg. Assume that the ions travel away from the spacecraft parallel to its direction of motion.</p>
</div>
<div class="specification">
<p>An initial mass of 60 kg of fuel is in the spacecraft for a journey to a planet. Half of the fuel will be required to slow down the spacecraft before arrival at the destination planet.</p>
</div>
<div class="specification">
<p>In practice, the ions leave the spacecraft at a range of angles as shown.</p>
<p style="text-align: center;"><img 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W+6w9qay+2OVrNMTldOG3G5W9VlclY13z4aF4eI/TAwIrVyGWJZITIOnQaChqGfvJHKjqvYvWI90sQhYAXK8j/DnKkHEPDhePR0ewxufr0R7PIj9iZlq5ZFPsKNE9uxdGEqytUkGkE+YBxCW/8Tq9ZkKMspfsXRpBTktZuMyGHeaNJzPKJ6HUfk4u2qIWLq6y+xYlE8MGMGhno1AsStfUehVVIM1mb+Kv4xVNzIxq49F+AtlVG3KZ3IjNRRKq/56YqWnq1UF/5AWdl/NX/kc70ElA/Vcq9O8JECWcVyqviSaqegjCmjt9EaLqpGA8p1nVl6CD8DTy/J8WwEef9h6H9lH1JO3hVlKn7Nwt7k5nhrSGe4QWWbi9xA7EwmDucq69WgkJ6fJR2VI3Rab7mijreRduhc5XSOrgQtO3R/5O/6CGgx1leAr1mKgPLB8m7wAmQ//R6yaDj5p8NY9nQ2pvcbh1gaHlMf2fhgxWE8MXanOORccDwazx6Yj5lbTinfHMtOYev0Jcj2/BCnxSHpfGTNb4y9Ycu03k7U4vjEMAGZN8Zs3oqJzb7G0A6qOIAOYfi62TgkLHkVz6r/D+qIkSO8cXnF3+HpIUfnwUfgs34HVoY8rxyuc+uBaUmL4PfDdAS0pTiCXlic1QyjEtdgpEtl8zL3PlgcvxkjK+KU5dr2w6qKEdgbPwl+FMwoex7Bq3YgLuAXLOnmrWwr+Gs0m7QV22Z0VQUqNoB74FxsSx6BihX98IJHG7zQLQ4VozZrlKlsU31mpI7q8uoTlXPzaBWC2r6EMfuK+S1NzcbAieIOruRpvPFWKSbFslT5oRYXXCD31AxeranqI9wsKdZwWquWL88rwU0FIHs2AMOHQPVAVq3K8XoNAzs3qaxkVOxMbXWUxKvydIj5RlR5R9oOQNSZSpdbKsmf9SPAqxvqx8+Ete/i5M4tON5rPr6VhgLhji7TlyPu1lCEL0vFwJQ30UJs8XmMnP8Ogr2UC6mUw4hPICnzPK7P6Ar59fM4crEVQvzlGg+NRfhajJA3ocpOIkrm7ofgWVsQPEufwdJ6wifg6T8EY8NGYaa+YuJQ5yhEpY9ClM7vgReGaF2RuXdFaHQaQqO1Lld+cfVCYFi0+K/you4ZDa3qbw9QrXSoIt9wHU0dlbE0YVoNknOzNP08lmpd5S8GCciaobVvcyDPUAnpTfm6oQJmuN4ALTzkcKkmSsbF1wMtRMe4Kfz6BgJTM5A7pwWupFyA7+BIyNVOMwCKnUkJg5fmNU2tNWbaNC8bd+6PyINbMZZGzvQe1TlgeivwRQMEDHWfgeJ82WwESs/hcPJtyF9pp5wrVDekGsrVmadW/yyeaJeRPdMevdr9iDWJ3+Bk5jdVMvpp1+VvTIAJGEOgsLAQuv/u3q3rsLnyIas3voRiWdAKni1djVHLhGWkKadifH/+lvZoUNl1FBVCY2RCVRaZ+Ff8PqSe8UGIf2tVkFs1tmnEztRN8ep0PIHYID8MTsjX1r1uDXEtFQF2EmzkVlDcLMG56kbKtILkalDatStmfpGKuC6/I23FXIT366STSriG+vyzFoEHDx4gLTVV6xp/cS4C165dQ1C//ggdOQqTJ05U/+sVEKC1FJXSbR87dswIODK4dRmO2T104kvEWJZ9aGUwdsQI0fUp4uaH0HmdkbUwChtO3FA+bGkVxrsLsLs1xcV4VUa7u3XG4AnN8cW67cjr1Bc91PE5MrgZEztTVz3demDKh910dMxH2kfR+BjjtHWsqQ0xRqGhslR5GdRxmDXVc6Lf2Umwkc6WtfBAB4256SpqVQkCqlJC+wINSYe8haj08yj66Rj2xgbi5spxGPrRUcNBPdoS+JuKQPL+/Thx4oQBHlKyo6Rqhj4NVOXLdkOgZcuW6NW7N+7cvo0rl0vU/x6Ua+986de1Czp37mycXRSRH6sTXzLzEvw3pmLPLCm+xDhRpivlBu+wFdi/0R+3FvcR41k8OyxEUcBypH8xTRkXo26sCTr/4zX4wh39x/1Ne6rBqNgZtaBanjTAsyHLdHRUxgmpY3eMlSgG+Q7FIzFPwmTsL9bJ/WCsHEcupy9XM1+zDIEKrRz4yvz36hz9ahU08+JL+wRo5s2ngg+EgvjRgrzdYiHjnqEM5JpylMJTU1KE8vJydUt8UpXA6dOnhd69egl37typ+iNfcSoCBQUFQod2PoKc9unQ86+zb0e+T5zqjnAOY3kkwWY8wKboMmYCuh1ZgaUfH1Mtk6PEJpGYntQcby8JMRwApGODcmllMCJT81Xr5GmZXBYOn4KWx3/9+g0MDArioXQdftJXmm+eNWMGYtatQ9OmTaXL/OmkBLy8vOD5gpde6xs2bIi9+/fxfaKXDl+0ZwLsJNhM7yk36lmbthz+tz5SLZPrjneLXkHcwXjM9NNYWlSDzjKvUdiUPA7NvgpDZ3GJkBydxWVyMVg8SLUkD8DkKZOxecsWcSh95IgRRs6l1tC4A/0cGRGB8eHh6NSpkwNZxabUhQAFLEYsWoTrv/6KBg1Vc9gqQY8//jiWRr0PciL4YAKORuB/aMDE0Yxie2pPgIKt4mJjIff0xNiwMKf/g7crKQk5OTnYsHFj7WFyDYchQP9fJO3ciYsXLmDGzJno//e/4x9Br+JKSeV64pGhoxEVXWU9qcMwYEOcmwA7Cc7d/1Wspyj+dbGxGD7iDQwfMdwph0/prXHShAnYl5zslPZXuSmc7AKtZsnOzsa2LVtEy6fPnInu3burKWRmZuKdqVNBQYsUqJi4YwcaN26s/p1PmIAjEWAnwZF600S20B/JxIRErF6xAmtiY8S3J2f5I0i2U5wGxSHwNIOJbig7EUN9f+Bf/xKd5B7+/nh9+HCD90BXv5fw3//+F1+lfwNa+cAHE3BUAuwkOGrPmsAuCtxbu2YNcrKz8cHy5VpvUyYQb5MiaN75uedaifEaNqkgK2VyAnSf792zV3SK58yfjz59+9Q43fbDDz/gqaeeqrGcyZVlgUzAwgTYSbAwcHtsjobfF0dEiKq/Hx3tsH8YaarlwIEDWL1mDQ8f2+ONWkud6b5OTUlB+jffOPX0Wi2xcXEnI8BOgpN1eH3MpSCuRQsWgIZi350926Hm66U4hJ27dvHwcX1uEjuoS/fx1199JY6QScGIzjKdZgfdwyraGAF2EmysQ2xdHWnedvbMWaCh2bFhY+3+rVuKQ3CWKRVbv8fMoR/18enTp8UVPCRfNxjRHG2yTCbgCATYSXCEXrSCDdI87t49n4tLw4JDQqyghWmaXLVypSho7rx5phHIUmyGgOTU0oqdmoIRbUZpVoQJ2BABdhJsqDPsURUapk9MSEBxUZFdvp0dOnRIXOq2PSHB7kdE7PH+MZfOkhNLK3SMDUY0ly4slwnYMwF2Euy592xId3tMxkQ7+/XyD8CR7CyOQ7Che6k+qnAwYn3ocV0mUJUAOwlVmfCVehCwl2RMNAz9VlgYxk+YgL59+9bDYq5qCwQ4GNEWeoF1cEQC7CQ4Yq9a2SZ6ANcnGRP9wR8zcpSVreDmzUWgqOSySUTTfVZdZkSTNMJCmICTE2AnwclvAHOaX5dkTOQg0DJLc2Y8lNr4Oj2d4xDMeQPoke3p0Qb1dRLovvr30aNGZUbUowJfYgJMoBYE2EmoBSwuWjcCNE9sTDIm2lRp29atMGeuAopDGDN6tLj7Je/aV7f+rE+t+jgJHIxYH/JclwnUjQA7CXXjxrXqQEB6g9eXjOmTTZ/gSGYGVq9da9YgQnJEXF1dYc9LNuuA3q6rSCtoKD04bd0d9OqrDpXIy647h5V3eALsJDh8F9uWgdK6dSkZ04g3RmDrli0oKSnhdMi21VVW14acStqm+e6dO3hj5Ein2mjM6vBZASagIsBOAt8KViFAQ8f0Vv/Jho3o+JfO2B4fz/EBVukJyzZa03SD5ER+vns3mjZrhtAxY5xiYzHL9gK3xgSMJ/CY8UW5JBMwHQF6GFy6dAlvjB6Nhw//EJcjcqpc0/G1N0lSvAFl8KTpKEfeSMze+ob1dW4C7CQ4d/9bxXopeJDml0eHhoo60NByXGysuPHO2LAwh91p0irAbbhRKfnR5o2bxMyI+5KTOd7AhvuLVXM+Ajzd4Hx9blWLz5w5g1kzZsDQZkr2kozJqhDtuHFpukGKN7h44YK490f/v/+dp5vsuF9ZdcclwE6C4/atzVlGDwZKkrRz92fVzjPTVER9kjHZnOGskEiAphTSv/lGXObazseH4w34vmACdkCAnQQ76CRHUJE2UvowOrpWORDoobJ2zRrQ0jdDIw+OwMbRbaDRoy/27hX7cfiIN/DaoNfMuszV0XmyfUzAkgTYSbAkbSdti3IgUEBaXZMkGZuMyUnx2qTZ5OBRVkRapUAH7ZHh7+8P33Y+9c64aJMGs1JMwEEJyBzULjbLBgjQtAE5CHl5Z0EpkFu2bFknrSgz4u49e8StqCdNmICIRYtADyE66C21f9++oLlu+qSgSD7qRoCcsfoe1B+rVq7Ey34voaCgQFylQH1Hm2g1bty4vuK5PhNgAhYmwCMJFgbuLM2RgzBn9mzR3NVr1pjsAUFyD/zrXzhw4ACioqPRJ7A37peWqrE+2aQJso7lmKw9tWAHPsnMzMSs6TPw2GOP4be7d7E1IR6BgYFGWUz9Qc7AsZxj4mgRxRoMHjIEfn5+elcpSIGLRgnnQkyACVidADsJVu8Cx1OA3vIjIyLg69sRk6dMNpuB9OYb1K+/lvyGDRsi9at/8hJKLSqGv1Bf0Vu/5tHYpTGOZGVpPeRphKa8vFz8V3L5sugY5J46hRPf/4A3Ro9CYO/eaNeuXY2jRewkaJLmcyZg+wQ4T4Lt95FdaSjlQKAANXM6CBIUcgoePnwofUWDhg3h4uKi/s4n1RO4c+cOyCl4UP5AXZDOdR2Hrq+8DLmnp1ima9euCPjrXxEyeHCtnbH67gCpVpJPmAATsAgBdhIsgtk5GpEchIUREeIctLmtpliF9h19kXvipLqpl7u9UuPbrLown4gOlaJCoUWisYsLktNSa+0AaAnhL0yACTgEAXYSHKIbrW+EsTkQTK1p4o4d+Pbbb3Ho4CH07dcXAwYMMHUTDi2PgknfHBeGpB078aC8HI8//jhChtR+hMBYSDzdYCwpLscEbIMAxyTYRj/YtRbkICxasACbt2zht0877UlalUCxBk+3aFFtoqv6msdOgn6CNArXtGlTDrjVj4evWpEAOwlWhO8ITdc3B4IjMGAbjCfAToJ+Vi936YK7t+8geMhg9OnTB926d9cKHNVfi68yAfMT4OkG8zN22BakHAi8KY/DdjEbZiECtBLoSEYG0pJTxH/UrF/XLggODhZXjtQ1x4iF1OdmHJgAOwkO3LnmMs1cORDMpS/LZQK2TqB9h/aik6CpJwXk0j9awdOy1XMYFByC8eHjeUpCExKfm50AZ1w0O2LHakByEDw8PGDKJEmORan21lC+AtoBk+I7iLGjHrwEUn/PduzUSf8PgLjE96eiYsRv2+bQ94ZBAPyDVQnwSIJV8dtX4xRcNefdd9ErsLdFciDYF526a0sZD8PDxokC6K2RlnXSqg1OY1x3pvZQk5zBX375BRfOnxedQ5lMBoVCezkq2UH3RGCfPli9ZjXfE/bQsQ6mIwcuOliHmsscKQfCjJkzERwSYq5mnFIu7TlBb4qax6qYtRg8eLDmJYc4d9bARRop+vnnn8UVJCdOnBB3xLxackXMVilmqnzuObWjqNvRcRs+xqsDB+pe5u9MwCIEeCTBIpjtuxH6w/68R2vertlM3ajrIFAzN2/cNFNrLNbcBPQ5BNRmD39/MXX1wH/8A1OmTq2S9Ouppk3FvTMk/dp6yhGfmFilnPQ7fzIBSxBgJ8ESlB2gjZh169CpmnlTBzDRaibQw0DTUaDh5eefb2U1fbhh4wnQCNvVq1fxU3ExLl68iM93fSY61OQQUPrq14cPx7uzZxu1nJHiEmiFAyW0Chv/FqbPmMHTC8Z3BZc0E3FdfTgAACAASURBVAF2EswE1tHEsoNgvh6lt8WQ1wahYaOGuPf77wgZMoSHl82Hu86SaUOx27dvazkEtKeF30sv4YUXXqiVQ6BPCVrhQJtmxcStM3oXTn1y+BoTMCUBjkkwJU0HleWs88iW7k56CNHmVLwm3tLktduTAgqvXLmCosIi5OWdxb++SYemQ+DTvj2ee+45k77pU7v0jzIv8sEEbIUAOwm20hM2rAc7CTbcOaxavQhQ/ADthEkrDAoKCsQ3edr++u+vBolbnXt6eaJ169acbrxelLmyPRNgJ8Gee89CurOTYCHQTtCMNe8lih+g6QLao0LfCoO2cjmaN2/ODoET3IdsovEE2EkwnpXTlrTmH3anhe6ghlvqXqKpG5ouuHnjht6AQo82bdCqVSse2nfQ+4zNMh0BdhJMx9JhJVnqD7vDAmTD1ARMfS/pTheUlJSI8QM0XUBZQSmg0BzxA2qD+IQJODgBdhIcvINNYZ6p/7CbQieWYZ8E6nMv6a4uyMnOhmZCIp4usM97grW2bQLsJNh2/9iEdvX5w24TBrASdkXA0OiA5uoCni6wqy5lZe2YADsJdtx5llKdnQRLkXaudjSXGuqLHaB0xS3c3Xl1gXPdFmytjRFwKCeBdtDz9vbmYCQT32TsJJgYqJOJ03QGJodPEPcr0JwqeO65VnjmGXcxdqBZs2b8/6+T3R9srm0TcIiMi7SLXtTSZbhSUoL0gwf4j4xt33OsnYUJ0NK/FR99hGPZOejTry/emT7d5AmbpCkCWmJ46+ZNMefAvXv3xDTFZO4bo0eBnAE6KFWxvr0LLIyFm2MCTMAIAnY9kiA5B79eu4b/+7//E80lJ8HLy8sI07mIsQR4JMFYUrZXjt7iA7r3ENM9S9q19vDA4cwM6Wu1n9IoABUqLy8XcwzQOSUeIieguKgIlHyINgCj/QqefPJJcUXBn11dxWkC3ayEfC9Vi5t/ZAI2R8AuRxL0OQc2R5YVYgI2QOD06dNaDgKpdOP6dXyy6RM88YSrmENAV01pKkC6TqMA0kGbFtER8Ne/iomHOI20RIY/mYBjErArJ4GdA8e8Cdkq8xKgXSUfPnxYpRFXV1eMDQurct3YXQurVDTiQlHJZSNKcREmwARshYDdTDfQvGov/wBb4WYRPWzlDyoPEVuku83SCE0X9PQPwG9376rl+3Xtgr1ffKH+zidMgAkwAUME7MZJIAMoOGrDxxuw9/PdeFD+QK9NHJOgF0u9LrKTUC98Vq9M/99s+fRTnP7xNDr/pTOmz5hh0t0La2Mg30u1oVXbsn+gMCEcQSvl2Hp8CQLdZLUVwOXVBBQozVyGgLBizD64FWO9YKdsFSgrPIytSXcxcMkIeNXhlrArJ0Hqv+qcBXYSJEqm++Q/7KZj6eyS+F5y9jvAXuzXdRIa2YviOnreRmbEUITnjUN6SlidnIQ6+BU6OljhK+23Hrk4EkeysjD2rbfQ2KWxFbTgJpkAE2ACTIAJODYBu3QSpC7RdRak6/zp2AQoPmX2u+/izTFj8OnmzaB5dz6YABOg6YZQePosQWapQoWjFIWZCYgMag8axfH0CEZkQiYKy6Tf6U2zFzyDP0Hmic8qy/lMQOzhQpSpoerKaY+BEQnILCxVl6h6QkPdmUiMCFa13QaeQRFIzJTkarT9/SeY6EP6Kcsk5d6AUkN6o1+CjqT39tWqMr0QmXlbbE5x4wSS1PL166S4kYu0mAnoKNqvjwEAxQ3kpsaodegYvg4HfvxVwyQdtqWZiPRpj8HbD+PkzggMVMnuGL4e32kxIQYHERveXWkbcU3eLnLuGJEJw/R02enaJnGpZKFUVsVUvAduKUcRkq4CZ5YhqK1uWQ3zqjm1aydBsktyFn7IPQVal82H4xKgqaZBA/+BtOQU5Pw7CyuXf4SZM2bYrcFkz66kJPEfnfPBBExHoBT5CfMxdGo2nn7/MApKLqPg+Ht4OmsBgl7fgFy1owDgzHqsSnPBm1/koagkH1kbPXBw/HvYmvs7PUFRlpuImVO/h2fsMVBAddFPBzH3TykIn5OMQsnf0FW87BS2Tl+CbM8PcZrqkNz5jbE3bBn2F/5RWfrMCkzfAkz8Lh9FJWeQPulP2D1kGuLEtqViZ5GW447ZPxSj4Hg8xnVpCsWvqXj7b9Nx9On3kPUTyT+GtZ7fY3rwEqT9+khZsewE4sbNwtd/egsHxDLEYDr+tOddzNxySuUE/Y7cddMwfPPvGJh2BkUlxciZ3wZnDuSgXGpe72c58t6PQ9oTY7BHZJKNuJaHMHF6opqt4tcvMS94MS4EbFUy+GEmnvpmC3ZfrE6yAmX5n+Hd4AXIlmz76TCWPZ2N6f3GIVaLi17FVBebIzB6P7aGPg90WoL0n44gKrB5dRX0/uYQToJkGTkLjRvz1IPEwxE/c3Nzq6z7z8nKAo0u2NtBuxr2CeyNJRGR4r+X/V4CXXPkw1ZW7DgyY7VtpblIWnkaAR9GYlpXd9Afe5l7d7yzdjlGXvkEUfsKVW/rAFyGYe68QfBypVIN4O7nDz+XSzhy9iYUeITrZ79Hvtcr6OHlphQvexaBy9JQlGZ4nltx/TyOXGwFf385XMVaDeAeuAhflyRhrJfGHL9LCKLefwtd3BsAcINXyDuYG3ob25NPa7xpP4/g0AHwdpVB5t4WbV3v4ujGGBzwmoS5b3eHu/gkc4N3WBTihuQicmMOSqFA6cmvsP1KIEaFvaIqQwz8MXqED/Izz+M6OTilp5Gy5TZGzn8HwaJ9Mrh6DcLc+cPgooap/8QldBbmhngr7ZO5w693Z7hc/B5518lJuS3qmNVrPpa+2V5ZxrU9xhL/agXfxcmdW3Cc6km2ydzRZfpyxIXexsfLUg07ZvrVrNdVu8qTUC9LubJDEPjfssoBUMmgRo3s0zFcHxeH+6XaA44fREdjUUSEZJpRnxfOn6+2nE/79gZ/5+ykBtHY+Q8KlOZmIK1cjtntnxYdBLVBrs/A0wtIK7qOMjRTX9Y60SrjhWc6vgLvpfHY8aUX+qACLfsGqBwKrVpaX2TPtEevdquwJvEbtO/bCGUtAxAoORmaJb06wUd0EKSLrmjp2QrlKzOQOy8AftJlzc/SczicfBUuQzzQQutVV7NuTwQGLsPZCzR0n4W072ikToHfTyYiKuks0Kmv+F3JqRVmt1S6MspmZHBt2QZyFGu2WsO5VCcTRdfKgBak423I57VTOyiiAJFtNV6CaJueelDahuTLuFamQIsatDHVz+wkmIoky7EIgb/27Ikn3Ny0Hq5e3i+YfC8CSxjzn1v/qdLM+bxzSExIqHK9ugu0WyIlRtJ3lJWVGZT322+/4V/fpKur/f3VIDz11FPq1MpPt2ghZlXUTa2srlCHE17dUAdodaryCDdLiqsdLi/PK8FNRQcjpMvg6jcNew52wuHsdKxaugv5VKvdaETOH4uhgV6qkQIdUa5dMfOLVHQ+9G+krVijGmLviJFLZ+HNYT3hpf+WrRRSXowrNx/pdxJUpcqTxsEvqbKK+sxFrjwtO4/EmeGIOlQK79DZmNilKZr0jcJez5UYvpIetn8ANXBSy7TQieJmCc5VNxthBBdTqspOgilpsiyzE6Appb379+GjD5eLewnQW/KcuXPM3q45Guj6clec+P57LdEjR48CZTy0xiFNdVy5cgU0YpP173+L+zN8vusz9d4MlJaZmJvScbCGrY7fZgO08JDDpZo3YRdf5Vu4cRN1NATfE8H0LywaFAz4z92bEBkWjqKE/Ybnul29EBhC/95CFAUHfrkbnywch6FF8ciKrsFBcZGjdYsGgEEFXeC7NBn7w7y1R0rUnUvBhssRldMNa3JWIPhZms6gg4L7fgZAjkTNnFSVLPYha+GBDi7AOUMt1sjFUMW6XWcnoW7cuJYVCdAQ+bb47VbUwDRN006I+fn5OHzgoCiwT/9+4u6IppFeeynS1IP0KUmI/uADMebj6tWr+Km4GLExMeIIBO3pENi7N2gko2XLllJx/rQJAjK4+fVGsMsBfH/+FsZ4PV/5IC27jqJCQD74Gf0jAEboL3P3Q/D40Ti5ZRrOldyBAs0r5RuqT3P2IWMw6mQqvtMcxShUDp97qZM/leFa0c9wGRIOP/U1HaFuHdBnSHOkfX8RN970xrPqKYffkRszHsMzX0N6yj9EOfDqqz2doSjHvTuqwEZInFRTBOpYCQXKrl2uxsXS0UffV0lHcVrHG6poDkDkXw746qtEYRmGbFNyIXtauj6mmg7JNCDEdJfVaE0nsj6SpCUxCcrADEU+EoPbo/qlIvVpT7OuaqnKkj3qoBBFYQIGe9Rt2YimZJOel+UjTb3kJxSJmlHCJm2IhZmbAAXZbv70U+RdvABamUPnthp4S05A9+7dMTo0FBs2bhR1pi2fiwqLMGb0aIwcMQKHDh0Ss6KamxvLN5KAmx9C53VG1sIobDihWlJIw+/vLsDu1pMROcyr5ge72JRq+V/QEqSpl/eVovC7DOSiP8L6t9ErR/n3MxiRqfmqVQTK2IDDp4D+4/4GufT0Kd+HVSu/VC3LpBUZkZie7IeoqT0qH6xVTG6OnlNnIeDICiz9+BhuiCssSlGYGoPIdcDbS0LgJWsKv76BcDmTgl1Hf1UGaSpu4OTHUYhMv1Ep0a0Hpnzoh7SpkUjMpxgh0vNLrFqxr9rpmkoBhs5UOibHYJXEgP5+r4zB7uqmE9AUXcZMQDcd20QuSc1VtgEyeXeEdLqNtKRvkS+uVCH712MVLXlUH6o4BvH7Hygr+6/6F2NPpG4ytrxly8m8MTbtPM5GB1Zzs5hKpbs4mRiNj09XrrmXeYUhpaRuy0ZMpZW2nD9QuC8Ks5PbYk0OLRfSiRLWLszf7IQAOQY0jWJPB+ncqVMnTJ4yGd9lZuK9hQtFh4FWaNAOk9LUha5NvLpBl4g5v1O0/wrs3+iPW4v74AVay99hIYoCliP9i2nwE1cyGNN+I3i9uRp7JzXB18GdVDkPOmHoV00wMWk+XlMP42vLknmNwqbkcWj2VRg6i3kE5Ogc/DWaTYrB4kEaIxvtBmO432WselkOT49OeD3LB7FpyzSmB7TlSt9kzw7CyrTl8L/1EQLaUv4DlU7JGzDdrwmt5YBbzylIiPLFiTB/lf2RyHpuNLbHjtZYudAAz4Ysw/71PsgeTPbJ0Xn6j/CbNM7gy76kQ02fSh3frmTw8mpc7jUWb3eqJnARMrh6j8JaLdu6492iVxB3MB4zRdvIPC8MXR2Lt7ABAzsQuzHYcb8P5i7211CrEeQDxiH00SoEtX0JY/YVV65o0ShV3amNpWWmkYT6pZCsztjqf7Nm29VrVvkrefSWz83OwWaVPcBn1ROgXA//PnoU62Jj0cPfX9xlUnf6onoJ/KvzELCHv7lm6A0aIR/8Nopm7TYcy2GGZusq0qojCdqZsLpjYsxXOH1DmiuiUR/N6QYpw1TdM2+JWbX0ZsdS3aw6mamqTjfQMJRmBjFDWbBCEZ95VCMTGNl2UCPLmYHuKitEZkJl9i6t7GQii5cQtDQbKN+B8I5yC03DGNCVLzMBPQRoRCQ4JARfp6eDghwnTZggjixIWTHJ4eSDCTgHAXqu9ELH8CTVdAA902i6YzXWPBqEwV3sY/TQek6CmAkrHJ/eGYj954pRVPIvzG1zGQcPacwV6b2T6ph5S3EVadMGY/hnf8LEg5RV6wy+CLiAmWJ2LjcjMlPVJgtWNj5YcRhPjN0pZicrOB6NZw/M18jwpccwcanOm5ie9RyWHaephHxkvf8csqeGYETMCZSJUy+nkL7UH3B5E1vPFltoGkapK2UF5IMJGEuApiPIWdiXnCxWGRgUJMYsGFufyzEB+yfQHD3fjkFU+yN4XZwOaAPPtoPxacVAJMRPqsV0j5VJCFY5KoR7GYsF33aLhYx7FRoa/EfIWNRTkA+KFwrocsUlIWGQj+C7KEO4J6jqtO4pRGT8x3Ad9S9KWcq6glBREC+E6Na9lyFEtPMRQuIvCRWCTtvUvFYdlbzJKcI1TZW16tVWR0lZicdMIfXaQ+kiaaDk1Hq0kFDwQBCEB0JB/GhBXoWbRhUznP7yyy/CG8OHC5s2bjKDdBbpDAQKCgqEqVOmCPLWHgKd88EEmIB9ELDSSMJd5B7KRLlXG7TUCp7RjMQ00nuSMm+p1vxW1lJl3krOQG5pOYqzDyEPreCpmVXLLRBRF84jxeA620ppkLJgvaKTPUvKgqVaxqNRQ+NUZZfBMhIP3cxjUgavn5UZvDQkWvKUItu3JyQgL+8sVq1cyRsqWRK+g7RFcQm0KoIOmoKgkSlpCsJBTGQzmIBDErCOk6C4gyt5yl28TEVVzLyl3uWLIl3bKefvTdSAsVmw6tRcjTxuq9Yi10m6SSrR8PHqNWvE5DpzZs/mP/Amoep8Qmh1A01BXLx4ETQFcebMGeeDwBYzATsiYB0nQdYMrX1rvxuVYa6UeetbcZczcYcycccx2hXsMoouLEOgoYQchgVW+UXKglXlB+mClAVL+l6bzxp5NEcHj2Z61yLXppn6liVHgRLr+Pp2BDkK9ripUn0ZcP36E6DgRrqPYtatw6wZM3h0qv5IWQITMBsB6zgJUCW5qDL8rsooVRtzVdmpiinzltaWpZR5ayg8gykxUyPI/fvCFzrD9qrVE8oyNTRqsB0pC5bu1EkN8rR+lnicwQXN1R2U1EPM+qUzTaJV1/JfaG18jx49xCQ67ChYnr89t6i5uoHyLNAqiCeecBNHFY4dO2bPprHuTMAhCVjJSaAkF+MR1esApr/7WTXZooxhbkzmLcpO1R8zxjbB7hWbkSk+iB/hxtF92HvmRVUGK814CH2ZqYzLgmWMxlXLyODWZThm9ziOyMXbcVLUT7maYs7UfWg1YwaGqtOFVq1tjSuUee+D5ctFR4GHjK3RA3VrkzZ16uLnp0qI0waj3hhZN0EmqkWjU+R0bt6yBXGxsYhYtIizNpqILYthAqYgYCUngbJFPY/gVTsQq14e0h0zT3pj4oxutbar5sxb1N6zCFyyGXtHPcCqbt7w9PBGwIoHGKnOzlVTZiojs2DVWntVBdpnPHYH4gJ+wRJRPzk6z7wE/42p2DOra51zrNdVHWPqUZpechSGBoeA3wKNIWb9MoODg/H73d/Uivxw/DgWLlig/m6tEwpspOBY2gdi2JAhvFzSWh3B7TIBHQI2lnFRRzv+ahcEaMqB8vcvjIhA3760RzsftkpAc7hf0rFBgwYY8vow8QFNW07/2dUVrVu3NstOj8Zk76SUzosjIiD39MSiiAib3c9C4sefTMCRCbCT4Mi9a0HbJEdh+Ig3xOFjCzbNTdWCgLfcExUVFVo12nrKsWHTJlw4f168XlBQYHCLaEulWKblkcn792Pb1q1igCPFL/DBBJiA5Qmwk2B55g7bIv1hp1UPtPphbNhYfgO0wZ5OSEhA9NJlWprt2b8PL730ktY16QvtxfDzzz/jXF4ecnJyxC2iJ02dgoC//hWdO3c2ex9TvAutgAh69VW8/c47Zm9Psps/mQATUBJgJ4HvBJMSkBwFEkp5FSgwjQ/bIkBbOu/9/HM0bNgIs96dhbZyudEKktOQm5uLFMp1cOECaOTotUGvgRJumeuge+rj9euR/s03PKpgLsgslwkYIMBOggEwfLl+BGi7YMrQGBUdbXfbINfPcuepTQ4DPbhpSsDYHR+NiUkwRFAaVRgfHo4hQ4eyA2oIFF9nAiYkYL3VDSY0gkXZHgFa1kbTDhSpzrkUbK9/TKERJUWipbCaOz6acwkjxSVI2RrfCgvj+8oUncgymEANBNhJqAEQ/1x3AuQoSLkU2FGoO0dbr0lTSprbQ7/s9xLSUlPNoraUrXH8hAno5R9gtnbMojwLZQJ2SICnG+yw0+xNZcqhMGbkKOzc/RkotwIfjk2ApiHWrlkDSty0cNEirXiF+kw36FIjx/PDDz7AU089hXdnz+ZpLV1A/J0JmIAAjySYACKLqJ4AOQbpBw9g0YIFnHSpelQO8av0tt+/f38xf4Zmoi3aT8VUBwVL0s6SUgImzXZM1QbLYQLOTuBPS5cuXersEGplf1k+0t4fj3+8tRBxsSfx5MAA/Pl0AtZnP4menZrjf2olzESFywrx3YatyG7eBR2bPQbQnhQhvfDm+fYY/TcPNDRRM/UR06xZM/Tt1w9vT52KBw/+QJeuXeojjuvaAYEXX3xRDGikJYxNmjQBfTfH0bFjR3U7t27dgp+fHx5//HFzNMUymYDTEeCRhFp1+R8o3BeF2cltsSYnH0UlSRjb4gJ2vLMRZ7Tz09RKav0KK1B6Mgkz1+VBrYLMG2PTzuNsdCDc6ifcpLXpzY8Cz2jVA61+4MPxCVDypZ27duHz3bvFPteX8dEUFKgdCqCkg4MaTUGUZTABJQF2Eup0J7jhSdfH6lTT2SvRUDTlTyBHYZo4qvDA2ZGI9lMugJSUFPFB6mjD5uQc0r4M1OfmPCiAcu68eaCgRkoTbq7gSXPawLKZgM0REKo97gkFGfFCxAAfQd7aQ5C39hFeXRQvZBTcU9a6lyFEtPMRQrYdEr5fFy74qsvsEk5df6gh+aFw/VSKEDO+m0qOhyAfsEhIyCgQ7muUEgQqt6uyvXbhQswh7TIV138Qdi4apF8fSVbFdeHUjkXCq6I+HoLv+DjhsI7Ory76WK2P76IMgSyquH5KSF0r2UH2DhIi4jOEgvsVglBxSUgYJHGg3zwE37AJwrh2ynORT7vFQsa9CkmLyk+J09r9wgG1fGJJnP4jFByKEyao5PiO3ySc0GKn2wcaOgkVwr2MxSruKp3IFpWukl2iIvcLhIz4SiZV+Es6bjsknDDErtKiep+Vl5cLmzZuEqZOmSLQuTMfZP/rw4ap/9940dNLWB+33uGQ3LlzR7Tx4MGDZrftl19+Ee+tRQsXCtQuH0yACdSNAAxXqxDun4oTXm03WUi4pHIKKq4JGYsHCfJB8UIBPQvFBws9nLoJE9blCNfp2v1LQio9xAfECafo4SpIcsKFuB+uC8pH6EPheka08GrrIULMqd9UKjwUrqXMFHzpwZxySbhP9S7tFCa06yZMSbki1qu4liJMaafRlnBPuBQ/WfBtN1NIvaZySiquCKmTuwnyAYuFVNEx0Ckj6SzZVXFTKCi+Jwj3fxBiBvSstEN0Gg4JSwb8RXh17Q8qZ+aBUBA/WpBrOgPSwzX+kso2PUSlNtW2kUNCssnp0LDn/jkhYXw3wXdyinBNBCXpXsmu4nqOEEfOlgZfpaMwWkgoeKBsXNdJkOSqHZCHwvUfNgkT2vlU2qZHR0Hqb3Vbemyr5yVyFN4YPlygP+rOetBDU+mEazicrT0c0nkiO3v36iXk5OSYvbvJ+UrauVNs7/Tp02ZvjxtgAo5IoJrphke4fvZ75Hu9gh5eqplt2m55WRqK0sLgpVHTJWg+lr7dHe50zdUbwfNmYeSVfUg5eRfAXZxM3oefh4zG2K7uUFZrAPeewzC802UcOXsTChpfUVzGwfgDQOgszA3xhitoa+YBGDWkAQ7Ef4dixW0c3RiDA16TMFdqC27wDotC3JBcRG7MQSmJKf4OCekNMHL+OwgW9XaD95ARCMYBJBy4rGwLgMuQERjs7QbInoZXW1eUnvwK268EYlTYK0o7aHdpd3+MHuGD/MzzuC4qWb+BIBe1bSS7EwJfag500rDHVY4eAXKUH/kRBWUKoDQXSStPI+DDSExTsZO5d8c7a5dj5JVPELWvUG2PYc0oZmEv1uR0Q9T7b6GLewMADeDedSJWbxyGn9etw/7CP9TVNXWEzB1+vTvD5eL3yLv+SF3GlCeUS+GNkSPF4WFnzaXwv2VlVZA+1bQpaCmhox20umHzli3iklhz9zdNP1Cyp5h168T9H3YlJTkaTraHCZidgMajXretBnim4yvwPhOPHV9mIzP1KArpwVXlcIH8lXbqB6v4s+sz8PS6jbRD51CK5giMPoKz0X64mflPcZ4wLXU7IgcOQdSZh2ppiuJjSD0DyD2fgav6qrKu6JSUncPh5Ktw8fVACy2tXdHSsxXKkzOQW1qO4uxDyEMreLaslAK3QERdOI+UMG+Vk6JuQHUig1vgMpy9sARdbmapdExGYsQIBC3N1i1soe8KlOZmIK1cjlfaP62tt8gXKC66jqqPF1317iL3UCbKvTrBR3QQpN9lcG3ZBnL8jKJrhqQYU0aSV/dPSsQjJV1ytPl4Y6j4tG+Phg2116C4ublp5RcwRo69lBGDGXd/ZjHHUMrUSBtUURyMuZ0Te+kH1pMJGENA63GrXUEGV79p2HMwCl1+T8eqmWMR1EEOz6AIJGYWGvFwAsrzSnBToUBZfhIm+nRCUNhWnPydHI3/hz6x2xHZydgHXaVm5Unj4OfRBhQlrfzXzjQP8rLzSAz3R+d+U/CpOAIiQ5O+Udi71B8ovIxreh2kSr1qPnPRcYBqqvEIN0uKUV5NMSXfagrQT4o7uJJ3u5pCt3Gu5I4RIxLViDDBT5RLgd74nDGXAj00N2z+BE+4KUfsaOvmHbsc861XWt1A/U17MFAyJAraNPdBAbOUU0Ff7gZzt83ymYA9E6ghRF8GV6+eCKZ/YdFQ3MjFP3dvQmRYOIoS9iPKr3rTxbd+FGL/vOU43isGRzeE4FnJLSnNRGRhOeBbvQztX13guzQZ+w2OCPyBQu0KRn6jpY3LEZXTDWtyViD4WRqSp+M2MiN+BmD8Lnmqiib4aIAWHnK4oNigrKqjKnqKypqhtW9zIE/Pb+Kl5ujg0QwyXDdUwGLX6Y2PlstRZPqMmTPFVL8Wa9zKDQUGBuLHs2esrIVlm6epgPv3y8TtxekBbomDRq1o5GbShAniDpa8pbklqHMb9kygBidB2zSZux+Cx4/GyS3TlG+fopNQrhr29q5ck192HUWFzRE8qwPcys6hqBCQD9aeklCU/Y47GuJlOr7w8QAADORJREFU8u4I6QSsEYfQJVl/oDAhHEFLgciDH6HPkOZI+/4ibrzpXels4HfkxozH8MzXkJ4SBrl/X/giXjmE7tVI2QIlFxo8BFGYi/RED41WpdMyXCv6GfDqqz0kryjHvTvmmYuXWjb8KYObX28EuxzA9+dvYYzX85VTDiJfYqqcmjE0WaCU3RR+fQPhknwGF248gpfaAVKg7NplFKMVQjSnZgwrZJFfaLkcOQqUl3/2zFkWaZMbsR4BekjPmT1bXPpJ8SmWOKScCh9ER4tt66aOtoQO3AYTsBcC1TgJqgf0HjnWxM1WBQGWovC7DOSiPyb2b6N++yxPisGqLs9gPgUc0rD9uwuQ1ms+vu3ZHJB1EB/uu/fsw9EBcxHo3gCKG8ewYfEKHCgHXCRSsjb4+6xR2BsWg7V9X8DiwGeBG9nYtecCvGdsxlCv5+AydRYC+q7A0o9b4H0xeLEUhakxiFwHvJ0cogymlPfHjLEpCF+xGX1epPaAG0f3Ye+ZF1VlTkstanyqHqRJKdh1tL/YtkxxAyc/jkJk+g0NJTWqSKdifEBDnKPv5WUoa+QKV2m0RCpT1083P4TO64zXF0ZhQ8soZfCiiu/u1pOxd5gXZBTgKcYW0IiDAuVl5WikhkoNy+DWZThm9whH5OLtaBlNwYuPoSz/M8yZug+tZiRgKDlTFPVpIwc5CqZM32sjZrEaeghQcCHlzaAESJ5enujbt6+eUqa/RO1Gf/CBGH9EI1cUE8P7ipieM0u0fwLVPM4awevN1dg7qQm+Du6kmv/vhKFfNcHEpPl4Tf1G6gLv0GD4XV6NHhQn0CEc2e3fx/5Vg1Rv+83R8+3VWPrSDwjv5i3K6RxxHM+Frsaa0Oc1CDaAe+BcbEsegYoV/fCCRxu80C0OFaM2Y9uMrmIwo+zZQViZthz+tz5CQFuKSVDpk7wB0/2aKGXRCowlm7F31AOsEtvzRsCKBxipWUajVVUluPWcgoQoX5wI8xfb9uwQiaznRmN77OhKR6ZKPXoGk3MzFI+WDsALPpOxv7hypYC+4rW7Rqs3VmD/Rn/cWtxHpddCFAUsR/oX0+Cn8kZkomN0H1H92qPj6L0o1o0vdW2PsbE7EBfwC5aITOToPPMS/DemYs8sJdva6cWlmYDpCIiOwtq1+DA62uJ7e9D0A622oFgYygJqifgI05FjSUzA/ATqtwskxRV0m4Zz86qLEzC/EdwCE2AC9k/gzJkz4lJFmm6i0SRLHuQc0PSDvp0rLakHt8UEbI1ANSMJtqYq68MEmIAjE6DA1YUREWLgqqXf6KXpB1794Mh3GNtWFwLsJNSFGtdhAkzALAQoJmH4iDfEgEJLOwpkEE8/mKVbWagdE6jfdIMdG86qMwEmYLsEIhYtwnPPtYKlVjzokuDpB10i/N1ZCfBIgrP2PNvNBGyYwKKICHHXSGvt5MjTDzZ8c7BqFiXAIwkWxc2NMQEmYCwBSp9sC8sTCwsL1cmXrDWyYSwzLscETE2AnQRTE2V5TIAJmIwAPaCD+vXHkewsi6940DSCph8o6RMdUdHRoDTPfDABZyDA0w3O0MtsIxOwUwKam0FZc1dMmn6g1NE9evTAsCFDQMs19R2fbt7MG0jpA8PX7JbAn5YuXbrUbrVnxZkAE3B4Aq1atcKDB3/g8893429/+xsef/xxq9ncsWNHdP7LX8R8Dk2aNMGLL76o1iUzMxPz58zF5cuXERwSrL7OJ0zAngnwdIM99x7rzgSciACteHjyyScxd948q1tN8RK0g+VTTz0FCrKkUQ7ab4QOcmK+/OZr0CgIH0zA3gmwk2DvPcj6MwEnISDFBdCQP+0gae2D9ElMSMR3hw/jP/+5hZ+vXFWr1Kt3b2yL367+zidMwF4JcEyCvfYc680EnIwAxQXQjo3btm61+B4P+lCTPrTagT41HQQqezwnBxR0yQcTsHcC7CTYew+y/kzAiQjQng60IdOYkaNsIkDwm6+/Ru6pU1V64OHDh4iNia1ynS8wAXsjwE6CvfUY68sEnJyArax4oLiE6dPexoPycr09cjQzg0cT9JLhi/ZEgJ0Ee+ot1pUJMAGRQPfu3cU9HiIjIqy2vfO4sWOr7Y0H5Q94NKFaQvyjPRDgwEV76CXWkQkwAb0EVq1cKV63xooHGkm4ePEijuUcQ2FhAXL+nYWnmjbFb3fvaumafvAAr3TQIsJf7IkAOwn21FusKxNgAloEbG3FAzkOV69exaWLF3H8+HHknjyFee/Nx+vDh2vpzV+YgL0QYCfBXnqK9WQCTEAvAcpRQFkQP1i+HDQNwQcTYAKmI8BOgulYsiQmwASsRIDe4CmZkbX3eLCS+dwsEzAbAQ5cNBtaFswEmIClCNDSyJ27PxN3jbTmHg+WspfbYQKWIsAjCZYize0wASZgdgK7kpKQk5OD1WvWiEmOzN4gN8AEHJwAjyQ4eAezeUzAmQhQumYPDw98vH69M5nNtjIBsxFgJ8FsaFkwE2AC1iDw9jvvoKSkBDSqwAcTYAL1I8DTDfXjx7WZABOwQQK84sEGO4VVsksC7CTYZbex0kyACdREgFc81ESIf2cCNRPg6YaaGXEJJsAE7JAAr3iww05jlW2OAI8k2FyXsEJMgAmYkgCveDAlTZblbAR4JMHZepztZQJORoBXPDhZh7O5JiXAToJJcbIwJsAEbJEAr3iwxV5hneyBAE832EMvsY5MgAnUmwCveKg3QhbghATYSXDCTmeTmYCzEuAVD87a82x3XQnwdENdyXE9JsAE7I4Ar3iwuy5jha1MgEcSrNwB3DwTYAKWJ8ArHizPnFu0TwI8kmCf/cZaMwEmUA8CvOKhHvC4qlMRYCfBqbqbjWUCTEAiwCseJBL8yQQME+DpBsNs+BcmwAQcnACveHDwDmbz6k2AnYR6I2QBTIAJ2DMBXvFgz73HupubAE83mJswy2cCTMCmCWiueCCHgQ8mwAQqCfBIQiULPmMCTMCJCfCKByfufDbdIAEeSTCIhn9gAkzAmQhIKx4+iI52JrPZViZQLQF2EqrFwz8yASbgTARoxcNvv/2GTzZ94kxms61MwCABnm4wiIZ/YAJMwBkJPHjwAAODgvDB8uXo3r27MyJgm5mAmgCPJKhR8AkTYAJMAGjcuDF27tqFRQsW4MyZM4yECTg1AXYSnLr72XgmwAT0EaAVDzSSMGvGDPCKB32E+JqzEODpBmfpabaTCTCBWhM4dOgQtm3Zgu0JCeIIQ60FcAUmYOcEeCTBzjuQ1WcCTMB8BPr27Ytegb0xZ/ZsUKwCH0zA2Qiwk+BsPc72MgEmUCsCk6dMFssnJiTWqh4XZgKOQICdBEfoRbaBCTABsxJYvWYN8vLOghIu8cEEnIkAOwnO1NtsKxNgAnUiQCseFi5ahG1bt+LYsWN1ksGVmIA9EuDARXvsNdaZCTABqxCQNoNKP3gAXl5eVtGBG2UCliTAIwmWpM1tMQEmYNcEpM2gJk2YoLU0koIaIyMiMPz11+3aPlaeCegS4JEEXSL8nQkwASZQAwGacqBkS5R0qWnTphj75pvIPXFSrPVD7inxWg0i+GcmYBcE2Emwi25iJZkAE7A1AhTEuO+LL3DvXimulpSI6jV2aYxPt23jdM621lmsT50J8HRDndFxRSbABJyZwMuvvIKCS/lqB4FYPCh/gKNHjjgzFrbdwQiwk+BgHcrmMAEmYH4CmZmZCOrXHw8fPqzS2OFDh6pc4wtMwF4JsJNgrz3HejMBJmAVAjTNMG2SMsGSPgV+KirG3bt39f3E15iA3RFgJ8HuuowVZgJMwJoEXP78ZzRq3BgNGzY0qEZ+fr7B3/gHJmBPBNhJsKfeYl2ZABOwOoHBgwfj1OkfsTUhHr1699brLBw6yFMOVu8oVsAkBHh1g0kwshAmwASclQAlWErauROff7Yb90tLRQytPTxwODPDWZGw3Q5EgJ0EB+pMNoUJMAHrEaCEShnffYfYmBhQXELexQu8vbT1uoNbNhEBdhJMBJLFMAEmwAQkAoWFhZy2WYLBn3ZNgJ0Eu+4+Vp4JMAEmwASYgPkIcOCi+diyZCbABJgAE2ACdk2AnQS77j5WngkwASbABJiA+Qiwk2A+tiyZCTABJsAEmIBdE2Anwa67j5VnAkyACTABJmA+AuwkmI8tS2YCTIAJMAEmYNcE2Emw6+5j5ZkAE2ACTIAJmI8AOwnmY8uSmQATYAJMgAnYNQF2Euy6+1h5JsAEmAATYALmI8BOgvnYsmQmwASYABNgAnZNgJ0Eu+4+Vp4JMAEmwASYgPkIsJNgPrYsmQkwASbABJiAXRNgJ8Guu4+VZwJMgAkwASZgPgLsJJiPLUtmAkyACTABJmDXBNhJsOvuY+WZABNgAkyACZiPADsJ5mPLkpkAE2ACTIAJ2DWB/w+LTNezwEce6wAAAABJRU5ErkJggg=="></p>
</div>
<div class="specification">
<p>On arrival at the planet, the spacecraft goes into orbit as it comes into the gravitational field of the planet.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the initial acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the maximum speed of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why scientists sometimes use estimates in making calculations.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the ions are likely to spread out.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what effect, if any, this spreading of the ions has on the acceleration of the spacecraft.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what is meant by the gravitational field strength at a point.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Newton’s law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting a spherical planet of uniform density.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>change in momentum each second = 6.6 × 10<sup>−6</sup> × 5.2 × 10<sup>4</sup> «= 3.4 × 10<sup>−1 </sup>kg m s<sup>−1</sup>» ✔</p>
<p>acceleration = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3.4 \times {{10}^{ - 1}}}}{{740}}">
<mfrac>
<mrow>
<mn>3.4</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>740</mn>
</mrow>
</mfrac>
</math></span> =» 4.6 × 10<sup>−4</sup> «m s<sup>−2</sup>» ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>(considering the acceleration of the spacecraft)</p>
<p>time for acceleration = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{30}}{{6.6 \times {{10}^{ - 6}}}}">
<mfrac>
<mrow>
<mn>30</mn>
</mrow>
<mrow>
<mn>6.6</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = «4.6 × 10<sup>6</sup>» «s» ✔</p>
<p>max speed = «answer to (a) × 4.6 × 10<sup>6</sup> =» 2.1 × 10<sup>3</sup> «m s<sup>−1</sup>» ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>(considering the conservation of momentum)</p>
<p>(momentum of 30 kg of fuel ions = change of momentum of spacecraft)</p>
<p>30 × 5.2 × 10<sup>4 </sup>= 710 × max speed ✔</p>
<p>max speed = 2.2 × 10<sup>3 </sup>«m s<sup>−1</sup>» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>problem may be too complicated for exact treatment ✔</p>
<p>to make equations/calculations simpler ✔</p>
<p>when precision of the calculations is not important ✔</p>
<p>some quantities in the problem may not be known exactly ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ions have same (sign of) charge ✔</p>
<p>ions repel each other ✔</p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the forces between the ions do not affect the force on the spacecraft. ✔</p>
<p>there is no effect on the acceleration of the spacecraft. ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>force per unit mass ✔</p>
<p>acting on a small/test/point mass «placed at the point in the field» ✔</p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>satellite has a much smaller mass/diameter/size than the planet «so approximates to a point mass» ✔ </p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">Three identical light bulbs, X, Y and Z, each of resistance 4.0 Ω are connected to a cell of emf 12 V. The cell has negligible internal resistance.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The switch S is initially open. Calculate the total power dissipated in the circuit.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The switch is now closed. State, without calculation, why the current in the cell will increase. </span></p>
<div class="marks">[1]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The switch is now closed. Deduce the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{power dissipated in Y with S open}}}}{{{\text{power dissipated in Y with S closed}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>power dissipated in Y with S open</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>power dissipated in Y with S closed</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>.</span></p>
<p> </p>
<p><span style="background-color:#ffffff;"> </span></p>
<div class="marks">[2]</div>
<div class="question_part_label">bii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">total resistance of circuit is 8.0 «Ω» ✔<br></span></p>
<p><span style="background-color:#ffffff;">P = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{{12}^2}}}{{8.0}}">
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>12</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>8.0</mn>
</mrow>
</mfrac>
</math></span> =18 «W» ✔</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">«a resistor is now connected in parallel» reducing the total resistance<br></span></p>
<p><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p><span style="background-color:#ffffff;">current through YZ unchanged and additional current flows through X ✔</span></p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">evidence in calculation or statement that pd across Y/current in Y is the same as before ✔<br></span></p>
<p><span style="background-color:#ffffff;">so ratio is 1 ✔</span></p>
<div class="question_part_label">bii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates scored both marks. ECF was awarded for those who didn’t calculate the new resistance correctly. Candidates showing clearly that they were attempting to calculate the new total resistance helped examiners to award ECF marks.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most recognised that this decreased the total resistance of the circuit. Answers scoring via the second alternative were rare as the statements were often far too vague.</p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very few gained any credit for this at both levels. Most performed complicated calculations involving the total circuit and using 12V – they had not realised that the question refers to Y only.</p>
<div class="question_part_label">bii.</div>
</div>
<br><hr><br><div class="specification">
<p>A photovoltaic cell is supplying energy to an external circuit. The photovoltaic cell can be modelled as a practical electrical cell with internal resistance.</p>
<p>The intensity of solar radiation incident on the photovoltaic cell at a particular time is at a maximum for the place where the cell is positioned.</p>
<p>The following data are available for this particular time:</p>
<p style="text-align: left; padding-left: 150px;"> Operating current = 0.90 A<br>Output potential difference to external circuit = 14.5 V<br> Output emf of photovoltaic cell = 21.0 V<br> Area of panel = 350 mm × 450 mm</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the output potential difference to the external circuit and the output emf of the photovoltaic cell are different.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the internal resistance of the photovoltaic cell for the maximum intensity condition using the model for the cell.</p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m<sup>−2</sup>.</p>
<p>A measure of the efficiency of a photovoltaic cell is the ratio</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>energy available every second to the external circuit</mtext><mtext>energy arriving every second at the photovoltaic cell surface</mtext></mfrac><mo>.</mo></math></p>
<p>Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>two</strong> reasons why future energy demands will be increasingly reliant on sources such as photovoltaic cells.</p>
<p><img style="display:block;margin-left:auto;margin-right:auto;" src="data:image/png;base64,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"></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>there is a potential difference across the internal resistance<br><em><strong>OR</strong></em><br>there is energy/power dissipated in the internal resistance <strong>✓</strong></p>
<p>when there is current «in the cell»/as charge flows «through the cell»<strong> ✓</strong></p>
<p><em><br>Allow full credit for answer based on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mi>ε</mi><mo>-</mo><mi>I</mi><mi>r</mi></math></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em><br>pd dropped across cell <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>6</mn><mo>.</mo><mn>5</mn><mo> </mo><mo>«</mo><mtext>V</mtext><mo>»</mo></math>✓</p>
<p>internal resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">=</mi><mfrac><mrow><mn>6</mn><mo>.</mo><mn>5</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>9</mn></mrow></mfrac></math> ✓</p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn><mo> </mo><mo>«</mo><mtext>Ω</mtext><mo>»</mo></math>✓</strong></p>
<p><em><strong><br>ALTERNATIVE 2</strong></em></p>
<p><em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ε</mi><mo>=</mo><mi>I</mi><mo>(</mo><mi>R</mi><mo>+</mo><mi>r</mi><mo>)</mo></math> so <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ε</mi><mo>=</mo><mi>V</mi><mo>+</mo><mi>I</mi><mi>r</mi></math> <strong>✓</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn><mo>.</mo><mn>0</mn><mo>=</mo><mn>14</mn><mo>.</mo><mn>5</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>9</mn><mo>×</mo><mi>r</mi></math> <strong>✓</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>2</mn><mo> </mo><mo>«</mo><mtext>Ω</mtext><mo>»</mo></math> <strong>✓</strong></p>
<p><em><br>Alternative solutions are possible</em></p>
<p><em>Award <strong>[3]</strong> marks for a bald correct answer</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>power arriving at cell = 680 x 0.35 x 0.45 = «107 W» <strong>✓</strong></p>
<p>power in external circuit = 14.5 x 0.9 = «13.1 W» <strong>✓</strong></p>
<p>efficiency = 0.12 <em><strong>OR</strong></em> 12 % <strong>✓</strong></p>
<p><em><br>Award <strong>[3] marks</strong> for a bald correct answer</em></p>
<p><em>Allow <strong>ECF</strong> for <strong>MP3</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«energy from Sun/photovoltaic cells» is renewable<br><em><strong>OR</strong></em><br>non-renewable are running out <strong>✓</strong></p>
<p>non-polluting/clean <strong>✓</strong></p>
<p>no greenhouse gases<br><em><strong>OR</strong></em><br>does not contribute to global warming/climate change <strong>✓</strong></p>
<p><em><strong><br>OWTTE </strong></em></p>
<p><em>Do not allow economic aspects (e.g. free energy)</em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A girl rides a bicycle that is powered by an electric motor. A battery transfers energy to the electric motor. The emf of the battery is 16 V and it can deliver a charge of 43 kC when discharging completely from a full charge.</p>
<p>The maximum speed of the girl on a horizontal road is 7.0 m s<sup>–1</sup> with energy from the battery alone. The maximum distance that the girl can travel under these conditions is 20 km.</p>
</div>
<div class="specification">
<p>The bicycle and the girl have a total mass of 66 kg. The girl rides up a slope that is at an angle of 3.0° to the horizontal.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The bicycle has a meter that displays the current and the terminal potential difference (pd) for the battery when the motor is running. The diagram shows the meter readings at one instant. The emf of the cell is 16 V.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>The battery is made from an arrangement of 10 identical cells as shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the time taken for the battery to discharge is about 3 × 10<sup>3</sup> s.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce that the average power output of the battery is about 240 W.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the component of weight for the bicycle and girl acting down the slope.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).</p>
<p>Calculate the maximum speed of the bicycle and the girl up the slope.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On another journey up the slope, the girl carries an additional mass. Explain whether carrying this mass will change the maximum distance that the bicycle can travel along the slope.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the internal resistance of the battery.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the emf of <strong>one</strong> cell.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the internal resistance of <strong>one</strong> cell.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>time taken <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.0 \times {{10}^4}}}{7}">
<mfrac>
<mrow>
<mn>2.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>4</mn>
</msup>
</mrow>
</mrow>
<mn>7</mn>
</mfrac>
</math></span></span>«= 2860 s» = 2900«s» ✔</p>
<p><em>Must see at least two s.f.</em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of E = qV <em><strong>OR</strong></em> energy = 4.3 × 10<sup>3</sup> × 16 «= 6.88 × 10<sup>5</sup> J» ✔</p>
<p>power = 241 «W» ✔</p>
<p><em>Accept 229 W − 241 W depending on the exact value of t used from ai.</em></p>
<p><em>Must see at least three s.f</em>.</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of power = force × speed <em><strong>OR</strong></em> <em>force × distance</em> = <em>power × time</em> ✔</p>
<p>«34N» ✔</p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<p><em>Accept 34 N – 36 N.</em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>66 g sin(3°) = 34 «N» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>total force 34 + 34 = 68 «N» ✔<br>3.5 «ms<sup>-1</sup>»✔</p>
<p><em>If you suspect that the incorrect reference in this question caused confusion for a particular candidate, please refer the response to the PE.</em></p>
<p><em>Look for ECF from aiii and bi.</em></p>
<p><em>Accept 3.4 − 3.5 «ms<sup>-1</sup>».</em></p>
<p><em>Award <strong>[0]</strong> for solutions involving use of KE.</em></p>
<p><em>Award <strong>[0]</strong> for v = 7 ms<sup>-1</sup>.</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«maximum» distance will decrease <em><strong>OWTTE</strong></em> ✔</p>
<p>because opposing/resistive force has increased<br><em><strong>OR</strong></em><br>because more energy is transferred to GPE<br><em><strong>OR</strong></em><br>because velocity has decreased<br><em><strong>OR</strong></em><br>increased mass means more work required «to move up the hill» ✔</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>V dropped across battery <em><strong>OR</strong></em> R<sub>circuit</sub> = 1.85 Ω ✔</p>
<p>so internal resistance = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4.0}{6.5}">
<mfrac>
<mn>4.0</mn>
<mn>6.5</mn>
</mfrac>
</math></span> = 0.62«Ω» ✔</p>
<p><em>For MP1 allow use of internal resistance equations that leads to 16V − 12V (=4V).</em></p>
<p><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{16}{5}">
<mfrac>
<mn>16</mn>
<mn>5</mn>
</mfrac>
</math></span> = 3.2 «V» ✔</p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em>:</p>
<p>2.5<em>r</em> = 0.62 ✔</p>
<p><em>r</em> = 0.25 «Ω» ✔</p>
<p><em><strong>ALTERNATIVE 2</strong></em>:</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{0.62}{5}">
<mfrac>
<mn>0.62</mn>
<mn>5</mn>
</mfrac>
</math></span> = 0.124 «Ω» ✔</p>
<p><em>r</em> = 2(0.124)= 0.248 «Ω» ✔</p>
<p><em>Allow ECF from (d) and/or e(i)</em>.</p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>This question was generally well answered. Candidates should be reminded on questions where a given value is being calculated that they should include an unrounded answer. This whole question set was a blend of electricity and mechanics concepts, and it was clear that some candidates struggled with applying the correct concepts in the various sub-questions.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates struggled with this question. They either simply calculated the weight, used the cosine rather than the sine function, or failed to multiply by the acceleration due to gravity. Candidates need to be able to apply free-body diagram skills in a variety of “real world” situations.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>This question was well answered in general, with the vast majority of candidates specifying that the maximum distance would decrease. This is an “explain” command term, so the examiners were looking for a detailed reason why the distance would decrease for the second marking point. Unfortunately, some candidates simply wrote that because the mass increased so did the weight without making it clear why this would change the maximum distance.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br>