A capacitor of capacitance C discharges through a resistor of resistance R. The graph shows the variation with time t of the voltage V across the capacitor.

The capacitor is changed to one of value 2C and the resistor is changed to one of value 2R. Which graph shows the variation with t of V when the new combination is discharged?

B

The root mean square (rms) current in the primary coil of an ideal transformer is 2.0 A. The rms voltage in the secondary coil is 50 V. The average power transferred from the secondary coil is 20 W.

What is $\frac{N_p}{N_s}$ and what is the average power transferred from the primary coil?

C

A fully charged capacitor is connected to a resistor. When the switch is closed the capacitor will discharge through the resistor.

Which graphs correctly show how the charge on the capacitor and the current in the circuit vary with time during the discharging of the capacitor?

A

The graph below shows the variation with time of the magnetic flux through a coil.

Which of the following gives three times for which the magnitude of the induced emf is a maximum?

A. 0, $\frac{T}{4}$, $\frac{T}{2}$

B. 0, $\frac{T}{2}$, T

C. 0, $\frac{T}{4}$, T

D. $\frac{T}{4}$, $\frac{T}{2}$, $\frac{3T}{4}$

B

This question was extremely well done, with the highest difficulty index seen on this paper.

Three identical capacitors are connected in series. The total capacitance of the arrangement is $\frac{1}{9}$mF. The three capacitors are then connected in parallel. What is the capacitance of the parallel arrangement?

A. $\frac{1}{3}$mF   

B. 1 mF

C. 3 mF

D. 81 mF

B

Why are high voltages and low currents used when electricity is transmitted over long distances?

A.  Cables can be closer to the ground.

B.  Electrons have a greater drift speed.

C.  Energy losses are reduced.

D.  Resistance of the power lines is reduced.

C

The diagram shows a bar magnet near an aluminium ring.

The ring is supported so that it is free to move. The ring is initially at rest. In experiment 1 the magnet is moved towards the ring. In experiment 2 the magnet is moved away from the ring. For each experiment what is the initial direction of motion of the ring?

B

The current I flowing in loop A in a clockwise direction is increasing so as to induce a current both in loops B and C. All three loops are on the same plane.

What is the direction of the induced currents in loop B and loop C?

C

Two identical circular coils are placed one below the other so that their planes are both horizontal. The top coil is connected to a cell and a switch.

The switch is closed and then opened. What is the force between the coils when the switch is closing and when the switch is opening?

C

A conducting ring encloses an area of 2.0 cm² and is perpendicular to a magnetic field of strength 5.0 mT. The direction of the magnetic field is reversed in a time 4.0 s. What is the average emf induced in the ring?

A. 0

B. 0.25 μV

C. 0.40 μV

D. 0.50 μV

D

The graph shows the variation of magnetic flux $\Phi$ in a coil with time $t$.

What represents the variation with time of the induced emf $\epsilon$ across the coil?

A

Candidate selections were divided across the options presented, with option B as the most common (incorrect answer). This suggests that candidates could use more guidance on how to interpret slope on a ɛ vs. t graph.

A conducting square coil is placed in a region where there is a uniform magnetic field. The magnetic field is directed into the page. There is a clockwise current in the coil.

What is a correct force that acts on a side of the coil?

D

The secondary coil of an alternating current (ac) transformer is connected to two diodes as shown.

Which graph shows the variation with time of the potential difference V_XY between X and Y?

A

A direct current (dc) of 5A dissipates a power P in a resistor. Which peak value of the alternating current (ac) will dissipate an average power P in the same resistor?

A.  5A

B.  $\frac{5}{2}\text{A}$

C.  $\frac{5}{\sqrt{2}}\text{A}$

D.  $\text{5}\sqrt{2}\text{A}$

D

A parallel-plate capacitor is connected to a cell of constant emf. The capacitor plates are then moved closer together without disconnecting the cell. What are the changes in the capacitance of the capacitor and the energy stored in the capacitor?

A

The graph shows the variation with time t of the current I in the primary coil of an ideal transformer.

The number of turns in the primary coil is 100 and the number of turns in the secondary coil is 200. Which graph shows the variation with time of the current in the secondary coil?

D

What are the units of magnetic flux and magnetic field strength?

B

Six identical capacitors, each of value C, are connected as shown.

What is the total capacitance?

A. $\frac{C}{6}$

B. $\frac{2C}{3}$

C. $\frac{3C}{3}$

D. 6C

B

Two capacitors of 3 μF and 6 μF are connected in series and charged using a 9 V battery.

What charge is stored on each capacitor?

A

Response C was an effective distractor as the most common answer selected by candidates, suggesting that candidates are not fully understanding capacitor rules in series and parallel.

A magnet connected to a spring oscillates above a solenoid with a 240 turn coil as shown.

The graph below shows the variation with time $t$ of the emf across the solenoid with the period, $T$, of the system shown.

The spring is replaced with one that allows the magnet to oscillate with a higher frequency. Which graph shows the new variation with time $t$ of the current $I$ in the resistor for this new set-up?

A

A capacitor of capacitance X is connected to a power supply of voltage V. At time t = 0, the capacitor is disconnected from the supply and discharged through a resistor of resistance R. What is the variation with time of the charge on the capacitor?

$\text{A. }\frac{X}{V}{e}^{-RXt}$

$\text{B. }\frac{X}{V}{e}^{-\frac{t}{RX}}$

$\text{C. }XV{e}^{-RXt}$

$\text{D. }XV{e}^{-\frac{t}{RX}}$

D

A circuit consists of three identical capacitors of capacitance C and a battery of voltage V. Two capacitors are connected in parallel with a third in series. The capacitors are fully charged.

What is the charge stored in capacitors X and Z?

C

A rectangular coil rotates at a constant angular velocity. At the instant shown, the plane of the coil is at right angles to the line $ZZ\mathit{\text{'}}$. A uniform magnetic field acts in the direction $ZZ\mathit{\text{'}}$.

What rotation of the coil about a specified axis will produce the graph of electromotive force (emf) $E$ against time $t$?

A.  Through $\frac{\mathrm{\pi }}{2}$ about $ZZ\mathit{\text{'}}$

B.  Through $\mathrm{\pi }$ about $YY\mathit{\text{'}}$

C.  Through $\frac{\mathrm{\pi }}{2}$ about $XX\mathit{\text{'}}$

D.  Through $\mathrm{\pi }$ about $XX\mathit{\text{'}}$

C

A coil is rotated in a uniform magnetic field. An alternating emf is induced in the coil. What is a possible phase relationship between the magnetic flux through the coil and the induced emf in the coil when the variations of both quantities are plotted with time?

B

A ring of area S is in a uniform magnetic field X. Initially the magnetic field is perpendicular to the plane of the ring. The ring is rotated by 180° about the axis in time T.

What is the average induced emf in the ring?

A.   0

B.   $\frac{XS}{2T}$

C.   $\frac{XS}{T}$

D.   $\frac{2XS}{T}$

D

A small magnet is released from rest to drop through a stationary horizontal conducting ring.

What is the variation with time of the emf induced in the ring?

C

A circular coil of wire moves through a region of uniform magnetic field directed out of the page.

What is the direction of the induced conventional current in the coil for the marked positions?

C

The circuit diagram shows a capacitor that is charged by the battery after the switch is connected to terminal X. The cell has emf V and internal resistance r. After the switch is connected to terminal Y the capacitor discharges through the resistor of resistance R.

What is the nature of the current and magnitude of the initial current in the resistor after the switch is connected to terminal Y?

C

The most common (incorrect) answer was response D, suggesting that candidates were uncertain of initial current magnitude while understanding that current would decrease upon discharge.

Three capacitors are arranged as shown.

What is the total capacitance of the arrangement?

A. 1.0F

B. 2.5F

C. 3.0F

D. 4.0F

A

A battery is used to charge a capacitor fully through a resistor of resistance R. The energy supplied by the battery is E_b. The energy stored by the capacitor is E_c.

What is the relationship between E_b and E_c?

A.  E_b < E_c

B.  E_b = E_c

C.  E_b > E_c

D.  The relationship depends on R.

C

Four identical capacitors of capacitance X are connected as shown in the diagram.

What is the effective capacitance between P and Q?

A.   $\frac{\text{X}}{3}$

B.   X

C.   $\frac{\text{4X}}{3}$

D.   4X

C

A diode bridge rectification circuit is constructed as shown. An alternating potential difference is applied between M and N.

Three statements about circuits are

I.   when diode P conducts, Q does not conduct
II.  when diode S conducts, neither P nor R conducts
III. the direction of conventional current in the resistor is from left to right.

Which statements are correct for this circuit?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A

A direct current $I$ in a lamp dissipates power P. What root mean square (rms) value of an alternating current dissipates average power P through the same lamp?

A.  $\frac{I}{2}$

B.  $\frac{I}{\sqrt{2}}$

C.  $I$

D.  $I\sqrt{2}$

C

This question was very challenging for HL candidates, with the lowest difficulty index on the paper. Option B was a very effective distractor; perhaps candidates were selecting their answer based on a connection between rms values and ${\left(\sqrt{2}\right)}^{-1}$.

The ratio $\frac{\text{number of primary turns}}{\text{number of secondary turns}}$ for a transformer is 2.5.

The primary coil of the transformer draws a current of 0.25 A from a 200 V alternating current (ac) supply. The current in the secondary coil is 0.5 A. What is the efficiency of the transformer?

A. 20 %

B. 50 %

C. 80 %

D. 100 %

C

An alternating supply is connected to a diode bridge rectification circuit.

The conventional current in the load resistor

A.  is a maximum twice during one oscillation of the input voltage.

B.  is never zero.

C.  has a zero average value during one oscillation of the input voltage.

D.  can only flow from P to Q.

A

Two capacitors of different capacitance are connected in series to a source of emf of negligible internal resistance.

What is correct about the potential difference across each capacitor and the charge on each capacitor?

C

A conducting bar with vertices PQRS is moving vertically downwards with constant velocity v through a horizontal magnetic field B that is directed into the plane of the page.

Which side of the bar will have the greatest density of electrons?

A.  PQ

B.  QR

C.  RS

D.  SP

D

A capacitor of capacitance 1.0 μF stores a charge of 15 μC. The capacitor is discharged through a 25 Ω resistor. What is the maximum current in the resistor?

A.  0.60 mA

B.  1.7 mA

C.  0.60 A

D.  1.7 A

C

The arrangement shows four diodes connected to an alternating current (ac) supply. The output is connected to an external circuit.

What is the output to the external circuit?

A.  Full-wave rectified current

B.  Half-wave rectified current

C.  Constant non-zero current

D.  Zero current

D

This was another challenging HL question, where candidate responses were divided across the options. Options A and B were most common, due perhaps to the fact that the presentation of this circuit looks like a rectifier. Candidates need to pay attention to the direction of the diodes when considering this type of circuit.

The diagram shows a diode bridge rectification circuit and a load resistor.

The input is a sinusoidal signal. Which of the following circuits will produce the most smoothed output signal?

C

The graph shows the variation of the peak output power P with time of an alternating current (ac) generator.

Which graph shows the variation of the peak output power with time when the frequency of rotation is decreased?

C

Three conducting loops, X, Y and Z, are moving with the same speed from a region of zero magnetic field to a region of uniform non-zero magnetic field.

Which loop(s) has/have the largest induced electromotive force (emf) at the instant when the loops enter the magnetic field?

A. Z only

B. Y only

C. Y and Z only

D. X and Y only

A

Three capacitors, each one with a capacitance C, are connected such that their combined capacitance is 1.5C. How are they connected?

C

Two initially uncharged capacitors X and Y are connected in series to a cell as shown.

What is $\frac{\text{voltage across X}}{\text{voltage across Y}}$?

A.  $\frac{1}{2}$

B.  $1$

C.  $2$

D.  $4$

C

A parallel plate capacitor is connected to a cell of negligible internal resistance.

The energy stored in the capacitor is 4 J and the electric field in between the plates is 100 N C^–1. The distance between the plates of the capacitor is doubled. What are the energy stored and the electric field strength?

A

A capacitor of capacitance $C$ has initial charge $Q$. The capacitor is discharged through a resistor of resistance $R$. The potential difference $V$ across the capacitor varies with time.

What is true for this capacitor?

A.  After time $\frac{RC}{2}$ the potential difference across the capacitor is halved.

B.  The capacitor discharges more quickly when the resistance is changed to $2R$.

C.  The rate of change of charge on the capacitor is proportional to $V$.

D.  The time for the capacitor to lose half its charge is $\frac{\ln 2}{RC}$.

C

X and Y are two plane coils parallel to each other that have a common axis. There is a constant direct current in Y.

X is first moved towards Y and later is moved away from Y. What, as X moves, is the direction of the current in X relative to that in Y?

C

A parallel-plate capacitor is connected to a battery. What happens when a sheet of dielectric material is inserted between the plates without disconnecting the battery? 

A. The capacitance is unchanged. 

B. The charge stored decreases. 

C. The energy stored increases. 

D. The potential difference between the plates decreases.

C

Three identical capacitors are connected together as shown.

What is the order of increasing total capacitance for these arrangements?

A.  P, S, R, Q

B.  Q, R, S, P

C.  P, R, S, Q

D.  Q, S, R, P

C

Option C was the most common selection, however all other options were effective distractors. This question would be useful in a review of combined capacitance when capacitors in series and parallel.

A transformer with 600 turns in the primary coil is used to change an alternating root mean square (rms) potential difference of 240 V_rms to 12 V_rms.

When connected to the secondary coil, a lamp labelled “120 W, 12 V” lights normally. The current in the primary coil is 0.60 A when the lamp is lit.

What are the number of secondary turns and the efficiency of the transformer?

D

The graph shows the power dissipated in a resistor of 100 Ω when connected to an alternating current (ac) power supply of root mean square voltage (V_rms) 60 V.

What are the frequency of the ac power supply and the average power dissipated in the resistor?

A

An alternating current (ac) generator produces a peak emf E₀ and periodic time T. What are the peak emf and periodic time when the frequency of rotation is doubled?

B

A resistor designed for use in a direct current (dc) circuit is labelled “50 W, 2 Ω”. The resistor is connected in series with an alternating current (ac) power supply of peak potential difference 10 V. What is the average power dissipated by the resistor in the ac circuit?

A. 25 W

B. 35 W

C. 50 W

D. 100 W

A

A capacitor is charged with a constant current $I$. The graph shows the variation of potential difference $V$ across the capacitor with time $t$. The gradient of the graph is $G$. What is the capacitance of the capacitor?

A.  $\frac{I}{G}$

B.  $\frac{G}{I}$

C.  $G\times I$

D.  $\frac{1}{G\times I}$

A

A rectangular flat coil moves at constant speed through a uniform magnetic field. The direction of the field is into the plane of the paper.

Which graph shows the variation with time t, of the induced emf ε in the coil as it moves from P to Q?

A

The graph shows the variation of an alternating current with time in a $4.0 \text{Ω}$ resistor.

What is the average power dissipated in the resistor?

A.  $4 \text{W}$

B.  $8 \text{W}$

C.  $16 \text{W}$

D.  $32 \text{W}$

B

Power $P$ is dissipated in a resistor of resistance $R$ when there is a direct current $I$ in the resistor.

What is the average power dissipation in a resistance $\frac{R}{2}$ when the alternating root-mean-square (rms) current in the resistor is $2I$?

A.  $P$

B.  $2P$

C.  $4P$

D.  $8P$

B

A current of 1.0 × 10^–3A flows in the primary coil of a step-up transformer. The number of turns in the primary coil is N_p and the number of turns in the secondary coil is N_s. One coil has 1000 times more turns than the other coil.

What is $\frac{N_{\text{p}}}{N_{\text{s}}}$ and what is the current in the secondary coil for this transformer?

A

The input to a diode bridge rectification circuit is sinusoidal with a time period of 20 ms.

Which graph shows the variation with time t of the output voltage V_out between X and Y?

A

Which two features are necessary for the operation of a transformer?

B

A capacitor is charged by a constant current of 2.5 μA for 100 s. As a result the potential difference across the capacitor increases by 5.0 V.

What is the capacitance of the capacitor?

A.  20 μF

B.  50 μF

C.  20 mF

D.  50 mF

B

Which of the following reduces the energy losses in a transformer? 

A. Using thinner wires for the windings. 

B. Using a solid core instead of a laminated core. 

C. Using a core made of steel instead of iron. 

D. Linking more flux from the primary to the secondary core.

D

The conservation of which quantity explains Lenz’s law?

A. Charge

B. Energy

C. Magnetic field

D. Mass

B

The plane of a coil is positioned at right angles to a magnetic field of flux density B. The coil has N turns, each of area A. The coil is rotated through 180˚ in time t.

What is the magnitude of the induced emf?

A. $\frac{BA}{t}$

B. $\frac{2BA}{t}$

C. $\frac{BAN}{t}$

D. $\frac{2BAN}{t}$

D