A Level Physics (A2) chapter 8: Capacitance MCQs with answers
By Team Megalecture · Updated 4 Nov 2026
72 exam-style questions on Capacitance, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.
Try each one, then open the answer. These ten stay the same; the test draws new ones every time.
1. An isolated metal sphere of radius 0.10 m carries a charge of 2.0 × 10−7 C. How much electric potential energy is stored?
A
1.8 × 10−3 J
B
3.6 × 10−3 J
C
0.018 J
D
1.8 × 104 J
Show answer
Answer: A. V = 8.99 × 109 × 2.0 × 10−7/0.10 = 1.8 × 104 V, so W = ½QV = ½ × 2.0 × 10−7 × 1.8 × 104 = 1.8 × 10−3 J. Leaving out the ½ gives 3.6 × 10−3 J; 1.8 × 104 is the potential in volts.
2. A 100 μF capacitor discharges through a resistor. The p.d. across it halves in 4.2 s. What is the resistance?
A
6.1 kΩ
B
29 kΩ
C
42 kΩ
D
61 kΩ
Show answer
Answer: D. The halving time is RC ln 2 = 0.693RC, so RC = 4.2/0.693 = 6.06 s and R = 6.06/100 × 10−6 = 61 kΩ. Taking 4.2 s as RC gives 42 kΩ; multiplying by ln 2 instead of dividing gives 29 kΩ.
3. A 100 μF capacitor charged to 12 V discharges through two 20 kΩ resistors connected in parallel with each other. What is the p.d. across the capacitor 2.0 s after the discharge starts?
A
0.22 V
B
1.6 V
C
4.4 V
D
7.3 V
Show answer
Answer: B. The two resistors in parallel give 10 kΩ, so RC = 1.0 s and V = 12e−2.0 = 1.6 V. Treating them as in series (40 kΩ, RC = 4.0 s) gives 7.3 V.
4. A charged capacitor discharges through a resistor. What is represented by the total area under the graph of current against time, from the start until the current is negligible?
A
the energy initially stored in the capacitor
B
the time constant of the circuit
C
the capacitance of the capacitor
D
the initial charge on the capacitor
Show answer
Answer: D. Charge = current × time, so the area under an I–t graph is the charge that has flowed, which is all of the initial charge Q0. Energy would be the area under a power–time graph.
5. For a capacitor discharging through a resistor, what is given by the gradient of the graph of charge on the capacitor against time at any instant?
A
the p.d. across the capacitor at that instant
B
minus the current in the resistor at that instant
C
the time constant of the circuit
D
the energy stored in the capacitor at that instant
Show answer
Answer: B. Current is the rate of flow of charge, so I = −dQ/dt during a discharge. The gradient is steepest (most negative) at the start, when the current is greatest.
6. A student finds the time constant of a circuit from τ = RC. The resistance is known to ±2% and the capacitance to ±10%. What is the percentage uncertainty in τ?
A
5%
B
8%
C
12%
D
20%
Show answer
Answer: C. For a product the percentage uncertainties add: 2% + 10% = 12%. Subtracting gives 8%. Electrolytic capacitors often have large tolerances, so C usually dominates.
7. Two 100 μF capacitors are connected in series, charged, and then discharged through a 20 kΩ resistor. What is the time constant of the discharge?
A
1.0 s
B
2.0 s
C
4.0 s
D
1.0 × 103 s
Show answer
Answer: A. In series the capacitance is 50 μF, so τ = RC = 20 × 103 × 50 × 10−6 = 1.0 s. Treating them as parallel (200 μF) gives 4.0 s.
8. A 220 μF capacitor charged to 9.0 V is connected across a 15 kΩ resistor. What is the current in the resistor 5.0 s later?
A
0.60 mA
B
0.47 mA
C
0.31 mA
D
0.13 mA
Show answer
Answer: D. I0 = V0/R = 9.0/15 000 = 0.60 mA and RC = 3.3 s, so I = 0.60 × e−5.0/3.3 = 0.13 mA. The current falls with the same time constant as the charge.
9. A 1.0 F supercapacitor is charged to 2.7 V. If all its stored energy could be used to lift a 0.50 kg mass, how high would the mass rise?
A
0.74 m
B
1.5 m
C
7.3 m
D
15 m
Show answer
Answer: A. W = ½CV2 = ½ × 1.0 × 2.72 = 3.6 J, and h = W/mg = 3.6/(0.50 × 9.81) = 0.74 m. Leaving out the ½ gives 1.5 m; leaving out g (using mass for weight) gives 7.3 m.
10. A student has four 4.0 μF capacitors and needs a combined capacitance of 10 μF, using all four. Which arrangement gives this?
A
all four connected in parallel
B
three connected in parallel, with the fourth in series with this group
C
two connected in series, and this pair in series with the other two connected in parallel
D
two connected in series, and this pair connected in parallel with the other two
Show answer
Answer: D. Two in series give 2.0 μF; in parallel with two more 4.0 μF capacitors this gives 2.0 + 4.0 + 4.0 = 10 μF. All in parallel gives 16 μF; three in parallel with one in series gives 3.0 μF.
72, each with the answer and a short explanation, across 3 topics: Capacitors and capacitance, Energy stored in a capacitor, Discharging a capacitor. Every chapter test draws ten of them, so you can take it many times.
Is the A Level Physics (A2) chapter 8 test free?
Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.
How is the chapter test marked?
The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.
