Practical skills in core practical 11

Collecting the data

• Use a data logger with a voltage sensor (high sampling rate for small RC), or an oscilloscope with a square-wave supply for RC of milliseconds.
• For hand timing, choose R and C so RC is tens of seconds, and read V at regular intervals.
• Fully charge before each discharge; use the same starting p.d.

Analysing it

• Quick estimate: RC is the time to fall to 37% of V_0 (or the time to halve divided by ln 2).
• Better: plot ln (V / V) against t / s. Gradient = -1/RC; intercept = ln V_0. A straight line confirms exponential discharge, and using all the points reduces random error.
• Compare RC with the nominal value from the labels. Capacitors often have tolerances of ± 10% or ± 20%, so use percentage difference or check against the tolerance range.

Safety

Give precautions specific to capacitors:

• discharge the capacitor fully before handling it;
• do not exceed its working (rated) p.d.;
• connect an electrolytic capacitor the right way round (correct polarity), as reverse connection can make it fail.

Insulating gloves are not accepted for ordinary laboratory power supplies.

Worked example

A 470 μF capacitor discharges through a 47 kΩ resistor. The measured RC is 19.8 s. Is this consistent with the labels if C has a ± 20% tolerance?

1. Nominal RC = 470 x 10^-6 x 47 x 10³ = 22.1 s
2. Percentage difference = |19.8 - 22.1| / 22.1 x 100 = 10%
3. This is well within the 20% tolerance of C.

Answer: Yes: the result is consistent with the labelled values

Check yourself

1. Find the nominal time constant of a 220 μF capacitor with a 100 kΩ resistor, in s.
   Show answer

   22 s. RC = 220 x 10^-6 x 1.00 x 10⁵ = 22 s.

2. A capacitor charged to 9.0 V discharges. What p.d. marks one time constant, in V, to 2 s.f.?
   Show answer

   3.3 V. V = 9.0 x e^-1 = 3.31 V (37% of 9.0 V).

3. The p.d. across a discharging capacitor halves in 15.2 s. Find RC in s, to 3 s.f.
   Show answer

   21.9 s. RC = 15.2 / ln 2 = 21.9 s.

4. A capacitor at 6.0 V discharges with RC = 22 s. Find the p.d. after 30 s, in V, to 2 s.f.
   Show answer

   1.5 V. V = 6.0 e^-30/22 = 1.53 V.

5. A graph of ln (V / V) against t / s has gradient -0.0455 s^-1. Find C in μF if R = 22 kΩ, to 3 s.f.
   Show answer

   999 μF. RC = 1 / 0.0455 = 21.98 s; C = 21.98 / 22000 = 999 μF.

6. Which precaution is specific to an experiment with an electrolytic capacitor?
   • Wear insulating gloves with a laboratory supply
   • Wear a lab coat
   • Connect it with the correct polarity and do not exceed its working p.d.
   • Work in a darkened room
   Show answer

   Connect it with the correct polarity and do not exceed its working p.d.. Reverse polarity or over-voltage can make an electrolytic capacitor fail.

7. When is an oscilloscope with a square-wave supply better than hand timing for capacitor discharge?
   • When RC is only a few milliseconds
   • When RC is several minutes
   • When the capacitor is uncharged
   • When there is no resistor
   Show answer

   When RC is only a few milliseconds. Changes over milliseconds are far too fast to read by hand.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)
• Pearson examiners' report: IAL Physics WPH16/01, June 2024

Last updated 8 November 2026. Spotted a mistake? Tell us.