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Capacitor discharge practical questions

Calculate capacitor discharge, interpret log-linear graphs and find capacitance and time constants.

Practise

Natural-log voltage ratio

For row 3, calculate ln(V/V₀), with V₀ = 8 V. Use natural logarithms. Give 3 significant figures.

Practical setup and assumptions

A capacitor initially at V₀ is disconnected from its charging supply and discharges through one resistor R. The voltmeter is ideal except in the separately stated loading task.

Assume R and C remain constant and there is no leakage. The readings follow V = V₀ exp(−t/RC). Use the table values without rounding intermediate results.

Readings for this dataset
Same-discharge readings
t / sV / V
08
0.54.8522452777
12.94303552937
1.51.78504128119
21.08268226589

The linked tasks use the same readings. These are generated practice data: treat them as exact unless an uncertainty is stated. Use the stated uncertainty rather than estimating it from scatter.

This answer has no unit.

Use decimals or e notation, e.g. 4.2e-3.

Hint

Divide the voltages before taking ln. The ratio is below 1, so its logarithm is negative.

Worked solution
  1. ln(2.94303552937/8) ≈ -1.
  2. The voltage ratio is dimensionless; a base-10 log gives a different number.
  3. Answer: -1.00 (no unit) (3 significant figures).
Next task in this dataset
Work through this dataset
  1. Convert R and C
  2. Voltage during discharge
  3. Charge remaining
  4. Discharge current magnitude
  5. Energy remaining
  6. Natural-log voltage ratio (current)
  7. Choose log-linear axes
  8. Signed log-linear gradient
  9. Capacitance from gradient
  10. Time to halve voltage
  11. Capacitance uncertainty
  12. Voltmeter loading

These tasks keep the same readings. Another question starts a new dataset. Your answers are checked separately.

Another question
Question type: Natural-log voltage ratio
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Discharge through a resistor

With the supply disconnected, V = V₀ exp(−t/RC). Convert kΩ to Ω and μF to F before finding RC. After one time constant, voltage is V₀/e. The time to halve is RC ln(2).

Charge, current and energy

Q = CV, current magnitude through the discharge resistor is V/R, and stored energy is ½CV². Voltage and charge have the same decay time constant; energy falls with voltage squared.

Use a natural-log graph

ln(V/V₀) is dimensionless. Plotted against time, it has gradient −1/(RC) and zero intercept. Base-10 logs give a different gradient. Capacitance is −1/(gradient × R), with R in Ω.

Check voltmeter loading

A finite-resistance voltmeter across the capacitor supplies a parallel discharge path. The effective resistance and time constant become smaller. Inferring C using nominal R then gives a value that is too low. Other tasks assume an ideal voltmeter, constant R/C and no leakage; they cover discharge only.

A-level relevance

AQA 7408: 3.7.4.1, 3.7.4.3–4; required practical 9 (selected); OCR A H556: 6.1.1–3 (selected). Tasks cover the selected skills listed above.

AQA specification · OCR A specification · AQA practical handbook · OCR practical skills handbook

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