Core Practical 11: Capacitor Charge and Discharge

Charge a capacitor from a low-voltage dc source through a resistor, then switch it to discharge through a known resistance. Measure voltage across the capacitor using a high-resistance voltmeter, data logger or oscilloscope. Record initial voltage, resistance, capacitor rating and sampling interval.

Choose RC long enough to resolve the voltage change with the available instrument. A manual meter is unsuitable if nearly all discharge occurs between readings. Discharge safely through an appropriate resistor before handling and observe polarity and voltage limits for electrolytic capacitors. The discharge loop must not accidentally remain connected to the supply.

For discharge, voltage falls as $V=V_0e^{-t/RC}$. Taking a logarithm gives a straight line: ln(V/Vref) against t has slope −1/RC. Vref is a fixed reference voltage, such as 1 V, so the logarithm is dimensionless. In routine numerical plotting “ln V” normally means using the numerical voltage in a stated unit.

Choose a useful voltage range; near zero the percentage uncertainty becomes large and a logger offset can dominate. Fit the line across the reliable range. A change of V0 moves the intercept but does not change the time constant if R and C remain fixed.

During charging, $V_C=V_s(1-e^{-t/RC})$, so log-linearise the remaining voltage difference Vs−VC rather than VC itself. At one time constant, discharge voltage is V0/e and charging voltage has reached about 63% of the final value.

A voltmeter with resistance comparable to the discharge resistor creates an extra parallel path, reducing effective resistance and the observed time constant. Capacitor leakage has a similar effect. Repeat with a second resistor and compare whether τ scales with effective resistance; repeated sampling alone cannot remove loading.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.