HL Paper 2
A fixed horizontal coil is connected to an ideal voltmeter. A bar magnet is released from rest so that it falls vertically through the coil along the central axis of the coil.
The variation with time t of the emf induced in the coil is shown.
Write down the maximum magnitude of the rate of change of flux linked with the coil.
State the fundamental SI unit for your answer to (a)(i).
Explain why the graph becomes negative.
Part of the graph is above the t-axis and part is below. Outline why the areas between the t-axis and the curve for these two parts are likely to be the same.
Predict the changes to the graph when the magnet is dropped from a lower height above the coil.
A device sends an impulse of electrical energy to maintain a regular heartbeat in a person. The device is powered by an alternating current (ac) supply connected to a step-up transformer that charges a capacitor of capacitance 30 μF.
The voltage across the primary coil of the transformer is 220 V. The number of turns on the secondary coil is 15 times greater than the number of turns on the primary coil.
The switch is moved to position B.
Explain the role of the diode in the circuit when the switch is at position A.
Show that the maximum energy stored by the capacitor is about 160 J.
Calculate the maximum charge Q0 stored in the capacitor.
Identify, using the label + on the diagram, the polarity of the capacitor.
Describe what happens to the energy stored in the capacitor when the switch is moved to position B.
Show that the charge remaining in the capacitor after a time equal to one time constant of the circuit will be 0.37 Q0.
The graph shows the variation with time of the charge in the capacitor as it is being discharged through the heart.
Determine the electrical resistance of the closed circuit with the switch in position B.
In practice, two electrodes connect the heart to the circuit. These electrodes introduce an additional capacitance.
Explain the effect of the electrode capacitance on the discharge time.
The following data are available for a natural gas power station that has a high efficiency.
| Rate of consumption of natural gas | = 14.6 kg s–1 |
| Specific energy of natural gas | = 55.5 MJ kg–1 |
| Efficiency of electrical power generation | = 59.0 % |
| Mass of CO2 generated per kg of natural gas | = 2.75 kg |
| One year | = 3.16 × 107 s |
Electrical power output is produced by several alternating current (ac) generators which use transformers to deliver energy to the national electricity grid.
The following data are available. Root mean square (rms) values are given.
ac generator output voltage to a transformer = 25 kV ac generator output current to a transformer = 3.9 kA Transformer output voltage to the grid = 330 kV Transformer efficiency = 96%
(i) Calculate the current output by the transformer to the grid. Give your answer to an appropriate number of significant figures.
(ii) Electrical energy is often delivered across large distances at 330 kV. Identify the main advantage of using this very high potential difference.
In an alternating current (ac) generator, a square coil ABCD rotates in a magnetic field.
The ends of the coil are connected to slip rings and brushes. The plane of the coil is shown at the instant when it is parallel to the magnetic field. Only one coil is shown for clarity.
The following data are available.
Dimensions of the coil = 8.5 cm×8.5 cm Number of turns on the coil = 80 Speed of edge AB = 2.0 ms–1 Uniform magnetic field strength = 0.34 T
(i) Explain, with reference to the diagram, how the rotation of the generator produces an electromotive force (emf ) between the brushes.
(ii) Calculate, for the position in the diagram, the magnitude of the instantaneous emf generated by a single wire between A and B of the coil.
(iii) Hence, calculate the total instantaneous peak emf between the brushes.
There is a proposal to power a space satellite X as it orbits the Earth. In this model, X is connected by an electronically-conducting cable to another smaller satellite Y.
Satellite Y orbits closer to the centre of Earth than satellite X. Outline why
The cable acts as a spring. Satellite Y has a mass m of 3.5 x 102 kg. Under certain circumstances, satellite Y will perform simple harmonic motion (SHM) with a period T of 5.2 s.
Satellite X orbits 6600 km from the centre of the Earth.
Mass of the Earth = 6.0 x 1024 kg
Show that the orbital speed of satellite X is about 8 km s–1.
the orbital times for X and Y are different.
satellite Y requires a propulsion system.
The cable between the satellites cuts the magnetic field lines of the Earth at right angles.
Explain why satellite X becomes positively charged.
Satellite X must release ions into the space between the satellites. Explain why the current in the cable will become zero unless there is a method for transferring charge from X to Y.
The magnetic field strength of the Earth is 31 μT at the orbital radius of the satellites. The cable is 15 km in length. Calculate the emf induced in the cable.
Estimate the value of k in the following expression.
T =
Give an appropriate unit for your answer. Ignore the mass of the cable and any oscillation of satellite X.
Describe the energy changes in the satellite Y-cable system during one cycle of the oscillation.
The diagram shows an alternating current generator with a rectangular coil rotating at a constant frequency in a uniform magnetic field.
The graph shows how the generator output voltage varies with time .
Electrical power produced by the generator is delivered to a consumer some distance away.
Explain, by reference to Faraday’s law of induction, how an electromotive force (emf) is induced in the coil.
The average power output of the generator is . Calculate the root mean square (rms) value of the generator output current.
The voltage output from the generator is stepped up before transmission to the consumer. Estimate the factor by which voltage has to be stepped up in order to reduce power loss in the transmission line by a factor of .
The frequency of the generator is doubled with no other changes being made. Draw, on the axes, the variation with time of the voltage output of the generator.
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.
The following data are available for the lamps when at their working temperature.
Lamp specifications 24 V, 5.0 W
Power supply emf 24 V
Power supply maximum current 8.0 A
Length of each rod 12.5 m
Resistivity of rod metal 7.2 × 10–7 Ω m
A step-down transformer is used to transfer energy to the two rods. The primary coil of this transformer is connected to an alternating mains supply that has an emf of root mean square (rms) magnitude 240 V. The transformer is 95 % efficient.
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.
Calculate the maximum number of lamps that can be connected between the rods. Neglect the resistance of the rods.
One advantage of this system is that if one lamp fails then the other lamps in the circuit remain lit. Outline one other electrical advantage of this system compared to one in which the lamps are connected in series.
Outline how eddy currents reduce transformer efficiency.
Determine the peak current in the primary coil when operating with the maximum number of lamps.
A small electric motor is used with a 12 mF capacitor and a battery in a school experiment.
When the switch is connected to X, the capacitor is charged using the battery. When the switch is connected to Y, the capacitor fully discharges through the electric motor that raises a small mass.
The battery has an emf of 7.5 V. Determine the charge that flows through the motor when the mass is raised.
The motor can transfer one-third of the electrical energy stored in the capacitor into gravitational potential energy of the mass. Determine the maximum height through which a mass of 45 g can be raised.
An additional identical capacitor is connected in series with the first capacitor and the charging and discharging processes are repeated. Comment on the effect this change has on the height and time taken to raise the 45 g mass.
The primary coil of a transformer is connected to a 110 V alternating current (ac) supply. The secondary coil of the transformer is connected to a 15 V garden lighting system that consists of 8 lamps connected in parallel. Each lamp is rated at 35 W when working at its normal brightness. Root mean square (rms) values are used throughout this question.
The primary coil has 3300 turns. Calculate the number of turns on the secondary coil.
Determine the total resistance of the lamps when they are working normally.
Calculate the current in the primary of the transformer assuming that it is ideal.
Flux leakage is one reason why a transformer may not be ideal. Explain the effect of flux leakage on the transformer.
A pendulum with a metal bob comes to rest after 200 swings. The same pendulum, released from the same position, now swings at 90° to the direction of a strong magnetic field and comes to rest after 20 swings.
Explain why the pendulum comes to rest after a smaller number of swings.
A cable consisting of many copper wires is used to transfer electrical energy from an alternating current (ac) generator to an electrical load. The copper wires are protected by an insulator.
The cable consists of 32 copper wires each of length 35 km. Each wire has a resistance of 64 Ω. The cable is connected to the ac generator which has an output power of 110 MW when the peak potential difference is 150 kV. The resistivity of copper is 1.7 x 10–8 Ω m.
output power = 110 MW
To ensure that the power supply cannot be interrupted, two identical cables are connected in parallel.
The energy output of the ac generator is at a much lower voltage than the 150 kV used for transmission. A step-up transformer is used between the generator and the cables.
Calculate the radius of each wire.
Calculate the peak current in the cable.
Determine the power dissipated in the cable per unit length.
Calculate the root mean square (rms) current in each cable.
The two cables in part (c) are suspended a constant distance apart. Explain how the magnetic forces acting between the cables vary during the course of one cycle of the alternating current (ac).
Suggest the advantage of using a step-up transformer in this way.
The use of alternating current (ac) in a transformer gives rise to energy losses. State how eddy current loss is minimized in the transformer.
Two capacitors C1 and C2 of capacitance 28 µF and 22 µF respectively are connected in a circuit with a two-way switch and a cell of emf 1.5 V with a negligible internal resistance. The capacitors are initially uncharged. The switch is then connected to position A.
The switch is moved to position B.
A cell is now connected by a switch to a coil X. A second coil Y of cross-sectional area 6.4 cm2 with 5 turns is looped around coil X and connected to an ideal voltmeter.
The graph shows the variation with t of the magnetic flux density B in coil Y.
Show that the charge stored on C1 is about 0.04 mC.
Calculate the energy transferred from capacitor C1.
Explain why the energy gained by capacitor C2 differs from your answer in (b)(i).
The switch is closed at time t = 0. Explain how the voltmeter reading varies after the switch is closed.
Determine the average emf induced across coil Y in the first 3.0 ms.
A student makes a parallel-plate capacitor of capacitance 68 nF from aluminium foil and plastic film by inserting one sheet of plastic film between two sheets of aluminium foil.
The aluminium foil and the plastic film are 450 mm wide.
The plastic film has a thickness of 55 μm and a permittivity of 2.5 × 10−11 C2 N–1 m–2.
The student uses a switch to charge and discharge the capacitor using the circuit shown. The ammeter is ideal.
The emf of the battery is 12 V.
Calculate the total length of aluminium foil that the student will require.
The plastic film begins to conduct when the electric field strength in it exceeds 1.5 MN C–1. Calculate the maximum charge that can be stored on the capacitor.
The resistor R in the circuit has a resistance of 1.2 kΩ. Calculate the time taken for the charge on the capacitor to fall to 50 % of its fully charged value.
The ammeter is replaced by a coil. Explain why there will be an induced emf in the coil while the capacitor is discharging.
Suggest one change to the discharge circuit, apart from changes to the coil, that will increase the maximum induced emf in the coil.
A negatively charged thundercloud above the Earth’s surface may be modelled by a parallel plate capacitor.
The lower plate of the capacitor is the Earth’s surface and the upper plate is the base of the thundercloud.
The following data are available.
Lightning takes place when the capacitor discharges through the air between the thundercloud and the Earth’s surface. The time constant of the system is 32 ms. A lightning strike lasts for 18 ms.
Show that the capacitance of this arrangement is C = 6.6 × 10–7 F.
Calculate in V, the potential difference between the thundercloud and the Earth’s surface.
Calculate in J, the energy stored in the system.
Show that about –11 C of charge is delivered to the Earth’s surface.
Calculate, in A, the average current during the discharge.
State one assumption that needs to be made so that the Earth-thundercloud system may be modelled by a parallel plate capacitor.
The electrical circuit shown is used to investigate the temperature change in a wire that is wrapped around a mercury-in-glass thermometer.
A power supply of emf (electromotive force) 24 V and of negligible internal resistance is connected to a capacitor and to a coil of resistance wire using an arrangement of two switches. Switch S1 is closed and, a few seconds later, opened. Then switch S2 is closed.
The capacitance of the capacitor is 22 mF. Calculate the energy stored in the capacitor when it is fully charged.
The resistance of the wire is 8.0 Ω. Determine the time taken for the capacitor to discharge through the resistance wire. Assume that the capacitor is completely discharged when the potential difference across it has fallen to 0.24 V.
The mass of the resistance wire is 0.61 g and its observed temperature rise is 28 K. Estimate the specific heat capacity of the wire. Include an appropriate unit for your answer.
Suggest one other energy loss in the experiment and the effect it will have on the value for the specific heat capacity of the wire.
A small magnet is dropped from rest above a stationary horizontal conducting ring. The south (S) pole of the magnet is upwards.
While the magnet is moving towards the ring, state why the magnetic flux in the ring is increasing.
While the magnet is moving towards the ring, sketch, using an arrow on Diagram 2, the direction of the induced current in the ring.
While the magnet is moving towards the ring, deduce the direction of the magnetic force on the magnet.
A capacitor consists of two parallel square plates separated by a vacuum. The plates are 2.5 cm × 2.5 cm squares. The capacitance of the capacitor is 4.3 pF.
Calculate the distance between the plates.
The capacitor is connected to a 16 V cell as shown.
Calculate the magnitude and the sign of the charge on plate A when the capacitor is fully charged.
The capacitor is fully charged and the space between the plates is then filled with a dielectric of permittivity ε = 3.0ε0.
Explain whether the magnitude of the charge on plate A increases, decreases or stays constant.
In a different circuit, a transformer is connected to an alternating current (ac) supply.
The transformer has 100 turns in the primary coil and 1200 turns in the secondary coil. The peak value of the voltage of the ac supply is 220 V. Determine the root mean square (rms) value of the output voltage.
Describe the use of transformers in electrical power distribution.
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.
When fully charged the space between the plates of the capacitor is filled with a dielectric with double the permittivity of a vacuum.
The switch S is initially open. Calculate the total power dissipated in the circuit.
The switch is now closed. State, without calculation, why the current in the cell will increase.
The switch is now closed. .
The cell is used to charge a parallel-plate capacitor in a vacuum. The fully charged capacitor is then connected to an ideal voltmeter.
The capacitance of the capacitor is 6.0 μF and the reading of the voltmeter is 12 V.
Calculate the energy stored in the capacitor.
Calculate the change in the energy stored in the capacitor.
Suggest, in terms of conservation of energy, the cause for the above change.
Two equal positive fixed point charges Q = +44 μC and point P are at the vertices of an equilateral triangle of side 0.48 m.
Point P is now moved closer to the charges.
A point charge q = −2.0 μC and mass 0.25 kg is placed at P. When x is small compared to d, the magnitude of the net force on q is F ≈ 115x.
An uncharged parallel plate capacitor C is connected to a cell of emf 12 V, a resistor R and another resistor of resistance 20 MΩ.
Show that the magnitude of the resultant electric field at P is 3 MN C−1
State the direction of the resultant electric field at P.
Explain why q will perform simple harmonic oscillations when it is released.
Calculate the period of oscillations of q.
At t = 0, the switch is connected to X. On the axes, draw a sketch graph to show the variation with time of the voltage VR across R.
The switch is then connected to Y and C discharges through the 20 MΩ resistor. The voltage Vc drops to 50 % of its initial value in 5.0 s. Determine the capacitance of C.
The diagram shows a sketch of an ideal step-down transformer.
The number of turns in the primary coil is 1800 and that in the secondary coil is 90.
State Faraday’s law of induction.
Explain, using Faraday’s law of induction, how the transformer steps down the voltage.
The input voltage is 240 V. Calculate the output voltage.
Outline how energy losses are reduced in the core of a practical transformer.
Step-up transformers are used in power stations to increase the voltage at which the electricity is transmitted. Explain why this is done.
A square loop of side 5.0 cm enters a region of uniform magnetic field at t = 0. The loop exits the region of magnetic field at t = 3.5 s. The magnetic field strength is 0.94 T and is directed into the plane of the paper. The magnetic field extends over a length 65 cm. The speed of the loop is constant.
Show that the speed of the loop is 20 cm s−1.
Sketch, on the axes, a graph to show the variation with time of the magnetic flux linkage in the loop.
Sketch, on the axes, a graph to show the variation with time of the magnitude of the emf induced in the loop.
There are 85 turns of wire in the loop. Calculate the maximum induced emf in the loop.
The resistance of the loop is 2.4 Ω. Calculate the magnitude of the magnetic force on the loop as it enters the region of magnetic field.
Show that the energy dissipated in the loop from t = 0 to t = 3.5 s is 0.13 J.
The mass of the wire is 18 g. The specific heat capacity of copper is 385 J kg−1 K−1. Estimate the increase in temperature of the wire.
X has a capacitance of 18 μF. X is charged so that the one plate has a charge of 48 μC. X is then connected to an uncharged capacitor Y and a resistor via an open switch S.
The capacitance of Y is 12 μF. S is now closed.
Calculate, in J, the energy stored in X with the switch S open.
Calculate the final charge on X and the final charge on Y.
Calculate the final total energy, in J, stored in X and Y.
Suggest why the answers to (a) and (b)(ii) are different.