CapacitanceAQA A-Level Physics: Topic test

20 questions, 54 marks

AQA A-Level Physics

Capacitance topic test

Total 54 marks

Name

Class

Date

1
A capacitor of capacitance 6.8 µF is connected across a 15 V d.c. supply until it is fully charged. The supply is then disconnected. Use ε₀ = 8.85×10⁻¹² F m⁻¹ where required.
(a)
What is the charge stored on the capacitor?
[1 mark]
A1.0×10⁻⁴ C
B4.5×10⁻⁷ C
C2.2×10⁶ C
D7.7×10⁻⁴ C
(b)
The capacitor remains disconnected and the plates are pulled apart so that the separation doubles (air between the plates). Which row describes what happens to the capacitance and to the charge on the plates?
[1 mark]
Acapacitance halves, charge halves
Bcapacitance halves, charge unchanged
Ccapacitance doubles, charge unchanged
Dcapacitance unchanged, charge halves
(c)
Calculate the energy stored by the capacitor when it is charged to 15 V.
[2 marks]
Total for question 1: 4 marks
2
A capacitor stores 4.0 mJ of energy when the potential difference across it is 20 V. It is part of a camera-trigger circuit and is charged by a variable power supply.
(a)
The graph of charge against potential difference for a capacitor is a straight line through the origin. What does the area under this graph represent?
[1 mark]
Athe capacitance of the capacitor
Bthe charge stored on the capacitor
Cthe energy stored in the capacitor
Dthe time constant of the circuit
(b)
What is the capacitance of the capacitor?
[1 mark]
A10 µF
B400 µF
C2.0 µF
D20 µF
(c)
Calculate the extra energy that must be supplied to the capacitor to increase the potential difference across it from 20 V to 30 V.
[2 marks]
Total for question 2: 4 marks
3
A parallel plate capacitor has square plates of side 0.21 m separated by 0.60 mm. The space between the plates is completely filled with a dielectric of relative permittivity 3.5 whose molecules are polar. Use ε₀ = 8.85×10⁻¹² F m⁻¹.
(a)
Calculate the capacitance of the capacitor.
[3 marks]
(b)
Explain how the polar molecules of the dielectric make the capacitance greater than it would be with a vacuum between the same plates.
[4 marks]
Total for question 3: 7 marks
4
A 100 µF capacitor charged to 12 V is discharged through a 220 kΩ resistor. A student wishes to use the discharge to determine the time constant of the circuit.
(a)
Calculate the time constant of the circuit and the potential difference across the capacitor 30 s after the discharge begins. Hence calculate the time taken for the energy stored in the capacitor to fall to one quarter of its initial value.
[6 marks]
(b)
Describe how the student could use measurements of potential difference and time during the discharge to find RC from a graph of ln V against t. State the expected gradient of the graph for this circuit and one way to reduce the uncertainty in the value of RC.
[6 marks]
Total for question 4: 12 marks
5
A parallel plate capacitor with air between its plates has capacitance C₀. A technician slides a sheet of dielectric of relative permittivity 4.0 into the gap so that it fills the gap completely, while the capacitor remains connected to a 9.0 V battery.
(a)
What is the capacitance once the dielectric fills the gap?
[1 mark]
AC₀/4.0
BC₀/2.0
C4.0 C₀
D16 C₀
(b)
How does the charge on the plates after the dielectric is inserted compare with the charge before?
[1 mark]
Afour times larger
Bunchanged
Cfour times smaller
Dsixteen times larger
(c)
The air-filled capacitance C₀ is 50 pF. Calculate the energy stored in the capacitor after the dielectric is inserted.
[2 marks]
Total for question 5: 4 marks
6
A 680 µF capacitor is allowed to discharge through a resistor. The potential difference across it falls from 8.0 V to 2.0 V in 9.0 s.
(a)
What is meant by the time constant of a discharging capacitor circuit?
[1 mark]
Athe time for the charge to fall to half of its initial value
Bthe time for the capacitor to discharge completely
Cthe time for the charge to fall to 1/e² of its initial value
Dthe time for the charge to fall to 1/e of its initial value
(b)
What is the time constant of the circuit?
[1 mark]
A2.3 s
B6.5 s
C13 s
D9.0 s
(c)
Calculate the resistance of the resistor.
[2 marks]
Total for question 6: 4 marks
7
A parallel plate capacitor is made from two circular metal discs of radius 6.0 cm separated by an air gap of 2.0 mm. It is connected to a 250 V supply and charged fully. Use ε₀ = 8.85×10⁻¹² F m⁻¹.
(a)
Calculate the capacitance of the capacitor.
[3 marks]
(b)
With the supply still connected, the gap is reduced to 1.0 mm. Calculate the increase in the energy stored in the capacitor.
[4 marks]
Total for question 7: 7 marks
8
An electronic timer uses a 22 µF capacitor that is initially uncharged. It is charged from a 5.0 V supply of negligible internal resistance through a 1.0 MΩ resistor, and a switch circuit operates when the potential difference across the capacitor reaches 3.0 V.
(a)
Calculate the time constant of the circuit, the time taken for the potential difference across the capacitor to reach 3.0 V, and the charging current at that instant.
[6 marks]
(b)
When the capacitor is fully charged, the supply has delivered a charge of 1.1×10⁻⁴ C. Calculate the energy transferred by the supply and the energy stored in the capacitor. Explain why they differ and state where the remainder goes.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).