3.7.4.4
Required practical: measuring capacitance from a discharge curve
Capacitance & Charge/Discharge — AQA A-Level Physics
Variables and equipment
- Independent variable: time t.
- Dependent variable: potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). V across the capacitor.
- Control variables: resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohms (Ω). R, initial p.d. V0.
- Equipment: capacitor, 10 kohm resistor, battery pack, voltmeterAn instrument that measures potential difference. Connected in parallel across the component. Has very high resistance. (0.1 V resolutionThe smallest change in a quantity that an instrument can detect. For example, a ruler has a resolution of 1 mm.), stopwatch (0.01 s), switch.
Method
- Charge the capacitor fully by connecting it to the battery. The voltmeterAn instrument that measures potential difference. Connected in parallel across the component. Has very high resistance. should read V0 (e.g. 10 V).
- Switch to the discharge circuit (disconnect battery, connect capacitor through resistor).
- Record voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference. every 10 s until V reaches approximately 0 V. Aim for 8-10 readings.
- The capacitor should be fully discharged before repeating.
Analysis: ln(V) against t
- Starting from V = V0 e^(-t/RC), take ln of both sides:
$$\ln V = -\frac{t}{RC} + \ln V_0$$
- This is $y = mx + c. Plot \ln(V)$ on the y-axis against t on the x-axis.
- $Gradient = -1/RC.$
- y-$intercept = \ln(V0)$.
- Calculate C from the gradient: $C = -1 / (R x gradient)$.
Evaluation
- Systematic errors: check voltmeterAn instrument that measures potential difference. Connected in parallel across the component. Has very high resistance. reads zero before starting. Use a digital voltmeter to avoid parallax.
- Random errors: use a large resistanceThe opposition to currentThe rate of flow of charge. Measured in amperes (A). flow. The ratio of potential difference to current. Measured in ohms (Ω). so the capacitor discharges slowly enough for accurate timing. A datalogger gives more precise voltageThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). Informal term for potential difference.-time readings than manual stopwatch.
- Safety: keep water away from electrical equipment. Capacitors can retain charge after powerThe rate of energy transfer. Measured in watts (W). is removed -- fully discharge before handling.
Examiner Tips and Tricks
- The ln(V) vs t graph should be a straight line with a negative gradient.
- If it curves, the data does not follow a true exponential -- check for systematic errors.
- The experiment can also be done by charging instead of discharging.