Topic questions Electricity Charging and discharging capacitors
11 questions · 82 marks · about 1.5 hours
The initial potential difference (p.d.) across a capacitor is V0. The capacitor is discharged through a resistor. The p.d. across the capacitor decreases to 
in 2 milliseconds.
Which of the following is equal to the time constant, in milliseconds, for this capacitor-resistor circuit?
A student is investigating circuits that include a filament bulb. The filament bulb is labelled ‘1.5 V, 0.50 W’.
Show that the resistance of the filament bulb when operating normally is about 5 Ω.
*(b) The student wishes to control the brightness of the filament bulb using a potentiometer. The student connects the circuit shown. The total resistance of the potentiometer is very much larger than the resistance of the filament bulb.
Explain how the brightness of the filament bulb changes as the potentiometer slider is moved from A to B.
The student connects the filament bulb in the circuit shown below. The capacitor is initially uncharged and has a capacitance of 1.2 F.
The resistance of the filament bulb is 5 Ω.
Explain how the brightness of the filament bulb will vary as the switch is closed.
A charged capacitor is discharged through a resistor. The potential difference across the capacitor halved in a time t. The time constant is T.
Which of the following is the equation for t?
A student investigated the discharge of a capacitor C through a resistor R using the circuit shown.
The student used the switch to connect C to X to charge the capacitor. She then connected C to Y to discharge the capacitor through R.
As the capacitor discharged, she recorded values of the potential difference V across C and corresponding values of time t. She used a stopwatch to measure t.
The student used her results to plot the following graph.
The capacitor was marked 220 μF ± 20%.
Deduce whether the student’s data give a value of capacitance within the stated range.
R = 82 kΩ
The student suggested that her results would have been more accurate if she had used a data logger to record the data.
Assess the student’s suggestion.
Also involves Discrete semiconductor devices
Power supplies provide either alternating or direct currents and potential differences.
A power supply produces an alternating potential difference (p.d.). The p.d. has a period of 0.02 s and a peak value of 4.0 V.
Calculate the frequency of the supply.
Calculate the root‑mean‑square p.d.
Root‑mean‑square p.d. =........
It is possible to convert alternating currents and p.d.s, to direct currents and p.d.s using diodes.
The power supply provides an input Vin to the circuit shown. The circuit includes four diodes D1, D2, D3 and D4 and a resistor R. The circuit produces an output
A graph of Vin against time and a corresponding graph of Vout against time are shown below.
Explain the operation of this circuit. Your answer should refer to D1, D2, D3 and D4.
A capacitor is added between points X and Y in the circuit.
The new graph of Vout against time is shown below.
Determine a value for the capacitance of the capacitor.
resistance of R = 2.2 kΩ
The diagram shows two parallel metal plates with a potential difference (p.d.) of 100 V across them. Three equipotential lines are shown.
Draw lines to represent the electric field in the shaded area.
A parallel plate capacitor consists of a thin layer of insulator of thickness d between two plates of conducting material of area A.
The capacitor has a capacitance 0.1 μF and is charged to a p.d. of 100 V by connecting it to an electrical supply.
The capacitor is then disconnected from the supply and the p.d. between the two plates slowly decreases. This is because the insulator is not perfect and a small charge can flow through it.
The graph shows how the p.d. varies with time.
The insulator is a type of plastic and should have a resistivity greater than 1014Ω m.
Deduce whether the plastic used in this capacitor has a resistivity greater than this value.
A = 5.6 
10−3m2
d = 0.6 
10−6m
The properties of capacitors make them useful in timing circuits.
The following circuit is used to provide an input Y to an integrated circuit.
Initially the capacitor is uncharged. The switch S1 is closed. Sketch a graph to show how the potential at point Y varies with time.
When the potential at Y is 8.0 V, the switch S2 is closed.
Calculate the time taken for the potential at Y to decrease to 2.0 V.
Calculate the energy stored on the capacitor when the potential at Y is 2.0 V.
When the potential at Y is 2.0 V, the switch S2 is opened. Calculate the power dissipated by the resistance R1 when the potential at Y is 2.0 V.
The properties of capacitors make them useful in timing circuits.
The following circuit is used to provide an input Y to an integrated circuit.
Initially the capacitor is uncharged. The switch S1 is closed. Sketch a graph to show how the potential at point Y varies with time.
When the potential at Y is 8.0 V, the switch S2 is closed.
Calculate the time taken for the potential at Y to decrease to 2.0 V.
Calculate the energy stored on the capacitor when the potential at Y is 2.0 V.
When the potential at Y is 2.0 V, the switch S2 is opened. Calculate the power dissipated by the resistance R1 when the potential at Y is 2.0 V.
Also involves Describing motion along a line
A ‘Gauss gun’ can be made from five ball bearings of equal mass and two magnets, as shown.
Pairs of ball bearings are placed to the right of two strong magnets. A single ball bearing is released from the left, as shown. The ball bearing is attracted to, and collides with, the first magnet. This and all subsequent collisions can be assumed to be elastic.
Explain what happens to make the last ball bearing on the right subsequently move off with a large velocity.
A student set up the apparatus shown to measure the speed of the last ball bearing. The ‘Gauss gun’ was placed at the end of a bench, so that the ball bearing left the gun and broke two strips of metal foil which formed part of an electric circuit.
As the ball bearing left the gun, it broke the first foil strip at its centre so that the capacitor started to discharge. When the ball bearing broke the second foil strip the capacitor discharge stopped.
Calculate the energy stored in the capacitor when it was fully charged.
The voltmeter reading halved in the time taken for the ball bearing to travel between the two foil strips.
Show that the time taken for the ball bearing to travel between the two foil strips was about 0.1 s.
The two foil strips were 0.50 m apart.
Calculate the horizontal velocity of the ball bearing.
The student positioned the second foil strip with its centre 8.0 cm lower than the centre of the first foil strip.
Deduce whether the ball bearing broke the second foil strip at its centre.
Assume the ball bearing was travelling horizontally as it broke the first foil strip.
A circuit consists of a battery of e.m.f. 5 V and negligible internal resistance, a switch, a 100 Ω resistor and an uncharged 50 µF capacitor.
Describe what happens to the potential difference across the resistor and the potential difference across the capacitor after the switch is closed.
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