Objective To investigate the relationship between the charge on a capacitor and the p.d. across the capacitor by charging at a constant rate.

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Topic

C8 Charging a capacitor at a constant rate (TAS)

Objective

To investigate the relationship between the charge on a capacitor and the p.d. across the capacitor by charging at a constant rate.

Apparatus

Capacitor, 500 μF
Microammter, 100 μΑ
Potentiometer100 kΩ
Clip component holder
Hand-held stop watch
CRO
Connecting leads

Procedure

Connect the following circuit. Set the CRO to d.c. and the sensitivity to 1 Vcm
Set the time base of the CRO to a high sweep rate so that a steady horizontal trace is displayed. Shift the trace to the bottom of the screen.
Short out the capacitor by connecting a connecting wire across it (XY). Adjust the 100 kΩ potentiometer to a suitable value for a steady current to flow (e.g. 80μA).
Remove the shorting wire and the capacitor will charge up.
Repeat the above procedure and record the time for the capacitor to charge up ...

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Procedure

Connect the following circuit. Set the CRO to d.c. and the sensitivity to 1 Vcm
Set the time base of the CRO to a high sweep rate so that a steady horizontal trace is displayed. Shift the trace to the bottom of the screen.
Short out the capacitor by connecting a connecting wire across it (XY). Adjust the 100 kΩ potentiometer to a suitable value for a steady current to flow (e.g. 80μA).
Remove the shorting wire and the capacitor will charge up.
Repeat the above procedure and record the time for the capacitor to charge up at a constant rate. The potentiometer must be adjusted to keep a constant current flowing in the circuit.
Measure the times for the CRO trace to move up by 1cm, 2cm, 3cm. The height is equivalent to the voltage across the capacitor. Tabulate the results.

Results

Discussion

When the shorting lead removed, the capacitor is being charged up. Moreover, the microammeter reading is being decreased and the CRO trace is being increased.

By the graph, it shows that p.d. is directly proportional to the time. It can be deduce that as the capacitor discharges, the p.d. across it decreases. The variation is linear.

When a capacitor is charged by connecting it to a battery or other dc power supply, the current in the circuit gradually falls to zero. The rate at which this happens depends on both the capacitance of the capacitor and the presence of any resistance in the circuit. If the resistance of the circuit is high, the current will be correspondingly small and the capacitor will charge up more slowly than if there were less resistance in the circuit.

Sources of errors

Error in keeping the current constant
Internal resistance of the cell
Non-zero value of the variable resistance when it is "minimum"

Conclusion

The microammeter reading is being decreased and the CRO trace is being increased when the shorting lead removed. It can be deduce that as the capacitor discharges, the p.d. across it decreases.