Inferring a capacitor’s discharge time

8 marks · A-level · original practice case

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The situation

A capacitor discharges through a 100 kΩ resistor. The ideal voltmeter has resolution 0.01 V. The table is simulated from exponential discharge with rounding to this resolution. Use the supplied model V = V₀ exp(−t/RC). Neglect leakage and loading.

Simulated voltage readings
t / s	V / V
0	5.00
10	3.03
20	1.84
30	1.12
40	0.68

Part (a)

Calculate ln(V/V₀) at t = 20 s using the displayed readings. [2 marks]

Give the numerical answer to 3 significant figures.

Final value (no unit)

Working

Part (b)

Determine the capacitance using that reading and the supplied model. [2 marks]

Give the numerical answer to 3 significant figures.

Final value / F

Working

Part (c)

Explain why voltage decreases by a smaller amount in each successive 10 s interval. [2 marks]

Your explanation

Part (d)

Evaluate using the late reading at 40 s to determine the time constant. [2 marks]

Your explanation

Marking rubric and worked answers

Indicative practice marks. Method marks assess valid working; accuracy marks require the associated valid method. Independent points stand on their own. Tick only points supported by your response. Do not award the same explanation twice. These ticks record your judgement, not an examiner’s result.

Part (a) marking points

Final answer: -1.00 (no unit). Numerical checks assess the final value only; they do not check working or the number of digits typed.

Form the dimensionless ratio 1.84/5.00. (1 method mark)
Use the natural logarithm to obtain −1.00. (1 accuracy mark)

No earlier numerical result is required. Award method credit for valid working and accuracy credit for the stated answer. Accept a defensible equivalent method; wrong physics cannot earn dependent accuracy credit.

Common errors: This uses base-10 log; the question specifies ln.

Part (b) marking points

Final answer: 2.00 × 10^-4 F. Numerical checks assess the final value only; they do not check working or the number of digits typed.

Rearrange ln(V/V₀) = −t/RC for C. (1 method mark)
Use R = 100000 Ω to obtain 2.00 × 10^-4 F. (1 accuracy mark)

Common errors: Check the kilo prefix when converting resistance to ohms.

Part (c) marking points

Discharge current V/R decreases as voltage falls. (1 independent mark)
Charge then leaves more slowly, so voltage falls more slowly. (1 independent mark)

Award each distinct physical point once. Equivalent scientifically correct wording is creditable; a contradictory statement cannot earn the same point.

Part (d) marking points

Its relative voltage resolution uncertainty is larger because voltage is smaller. (1 independent mark)
This makes the logarithm/time-constant inference more sensitive to voltage rounding. (1 independent mark)

Award each distinct physical point once. Equivalent scientifically correct wording is creditable; a contradictory statement cannot earn the same point.

Acceptable alternatives: A fitted log graph across several readings can reduce random reading effects; systematic effects still need consideration.

Report a problem with this case

Related skills

capacitor discharge practice

Scope and reference sources

AQA 3.5 and selected 3.7.3/3.7.4; OCR A Modules 4/6 (selected). These are shared original exercises; wording, indicative marks and difficulty have not been endorsed by either board.

AQA specification · OCR A specification

Case reference: capacitor-evidence · version 1.1.0 · seed 0. Choose another case