Wait, What? A discharging capacitor can keep losing voltage forever in the equation, yet your voltmeter reaches zero anyway.
The exponential model never predicts an abrupt end. Instead, voltage falls by the same fraction in each equal interval of time. Eventually the remaining signal becomes smaller than instrument resolution, electrical noise and leakage effects. The practical therefore teaches more than capacitor physics: it teaches how a continuous mathematical model meets a finite measuring instrument.
The experimental job
For a capacitor discharging through a resistor:
V = V₀e−t/RC
The product RC is the time constant τ. After one time constant, the voltage has fallen to about 37% of its initial value. After two, it is about 14%; after three, about 5%.
The Institute of Physics uses this exponential-discharge structure explicitly in A-level capacitor teaching, including the interpretation of CR as the time constant. See IOPSpark Episode 129: Discharge of a capacitor.
Why initial conditions matter
If the capacitor is supposed to begin at 6.0 V, it must actually reach a stable 6.0 V before discharge starts. Starting one run at 5.8 V and another at 6.2 V makes direct voltage comparisons unfair.
Charge for long enough relative to the charging time constant, confirm the initial voltage and use a consistent switching method. A clean experiment begins before the stopwatch starts.
The voltmeter changes the circuit
A real voltmeter has finite input resistance. When placed across the capacitor, it provides an additional discharge pathway. If meter resistance is not extremely large compared with the intended resistor, the effective resistance is lower than R and the observed time constant is reduced.
This is a powerful measurement principle: an instrument can perturb the system it measures.
Component labels are not exact values
A resistor labelled 100 kΩ may have a tolerance of several percent. Electrolytic capacitors can have even larger capacitance tolerances and may also show leakage. If you compare measured τ with nominal RC, disagreement does not automatically mean the exponential model failed.
Where possible, measure R with a multimeter and use the experimentally determined time constant to infer an effective C, or vice versa.
Two ways to determine the time constant
Method 1: the 37% method. Record V₀, calculate 0.37V₀, then find the time when the curve reaches that voltage.
Method 2: linearisation. Take natural logarithms:
ln V = ln V₀ − t/RC
A graph of ln V against t should be linear with gradient −1/RC. This uses many data points and can reveal systematic departures from the model.
Quantitative window
Suppose R = 220 kΩ and C = 470 μF.
τ = RC = 220000 × 470 × 10⁻⁶ ≈ 103 s
If V₀ = 5.0 V, after one τ:
V ≈ 5.0/e ≈ 1.84 V
If the measured 1.84 V point occurs at 94 s instead of 103 s, possible explanations include resistor/capacitor tolerance, meter loading, leakage or timing uncertainty.
Why early and late data can behave differently
Early in the discharge, the voltage is large and easy to measure, but switching delay can be significant. Late in the discharge, switching matters less but instrument resolution, background offsets and capacitor leakage become a larger fraction of the signal.
A strong analysis does not treat every data point as equally trustworthy.
Observation versus inference
Observation: “Voltage fell from 5.02 V to 1.86 V in 96 s.”
Transformation: “The ratio 1.86/5.02 ≈ 0.37.”
Inference: “The observed time constant is about 96 s.”
Further inference: “The circuit is broadly consistent with exponential RC discharge over this region.”
Failure modes
- Meter input resistance too low: the capacitor discharges faster than intended.
- Capacitor not fully charged: V₀ varies between trials.
- Manual switching delay: early-time measurements are shifted.
- Nominal R and C treated as exact: expected τ is overconfident.
- Recording too few late points: exponential character is weakly tested.
- Taking ln of noisy near-zero values: uncertainty is greatly amplified.
Unfamiliar transfer: charging instead of discharging
For charging toward supply voltage Vs:
V = Vs(1 − e−t/RC)
After one time constant, the capacitor has reached about 63% of its final voltage. The same RC controls both charging and discharging because the same resistance-capacitance combination sets how fast charge rearranges.
Secondary → JC → deeper Physics
Secondary: recognise that capacitors charge and discharge over time and understand simple energy-storage behaviour.
JC: use exponential equations, determine τ from graphs, linearise data, compare measured and nominal RC, and evaluate meter loading.
Deeper Physics: RC systems extend to differential equations, filters, sensor response, transient circuits, impedance and instrumentation bandwidth.
Checkpoint
A student uses a 1 MΩ discharge resistor and a voltmeter whose input resistance is also 1 MΩ. Will the observed time constant be approximately RC using the labelled 1 MΩ resistor?
Answer key and WHY reasoning
No. The voltmeter is effectively in parallel with the resistor, giving an effective resistance of about 0.5 MΩ. The observed τ will therefore be roughly half the naive RC value, assuming other effects are small.
How to study this practical
Practise moving between four representations: circuit diagram, exponential equation, V–t curve and lnV–t straight line. Then attach one experimental assumption to each symbol: R must be known, C may have tolerance, V must be measured without excessive loading and t must be referenced to a reproducible switch event.
Evidence boundaries
A school RC experiment supports an exponential lumped-component model over the measured voltage and time range. Real capacitors can have leakage, equivalent series resistance, dielectric absorption and voltage-dependent behaviour that the simple model does not capture.
Authoritative next steps
- Institute of Physics: Discharge of a capacitor
- Institute of Physics: supporting A-level practical requirements
- SEAB A-Level syllabus directory
Teaching Guide
For teachers and parents: ask students why a perfect-looking exponential curve can still give the wrong RC. Then introduce meter loading or component tolerance and require them to predict the direction of the error. The target is experimental diagnosis, not curve recognition.