Charging a capacitor at a constant rate

Experiment P: Charging a capacitor at a constant rate

Marks : ______________

Aim: To investigate how the charge on a capacitor is related to the p.d. applied across it by charging the capacitor at a constant rate.

Apparatus:

Capacitor (electrolytic type) 500 μF
Microammeter 100 μA
Clip component holder
Stop-watch
CRO
Connecting leads

Theory:

From definition, the capacitor C of a capacitor is found from

C = Q/V

Where Q is the charge stored on the capacitor and V is the potential difference across it.

⇒ Q = CV

⇒

If a capacitor is charged up at a constant rate, i.e. , where I is a constant.

Then is also constant.

Hence the potential difference across the capacitor increases linearly with time.

Procedure

The circuit was connected as shown in the figure below. The CRO was set to d.c. and the sensitivity to 1 V/cm.

The time base was set to any high value so that a steady horizontal trace is displayed. The trace was shifted to the bottom of the screen.
The capacitor was shorted out by connecting a lead across it and adjust the 100 k Ω potentiometer for a suitable ...

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Then is also constant.

Hence the potential difference across the capacitor increases linearly with time.

Procedure

The circuit was connected as shown in the figure below. The CRO was set to d.c. and the sensitivity to 1 V/cm.

The time base was set to any high value so that a steady horizontal trace is displayed. The trace was shifted to the bottom of the screen.
The capacitor was shorted out by connecting a lead across it and adjust the 100 k Ω potentiometer for a suitable current, say 80 μA.
Shorting lead was removed and the capacitor will charge up. Note what happens to the microammeter reading and the CRO trace.
The procedure was repeated but this time start the stop-watch and continuously adjust the potentiometer to keep the current constant as the capacitor charges up.
The times was measured for the CRO trace to move up by 1 cm, 2 cm, 3 cm, etc. These are the times for the p.d. across the capacitor to reach 1V, 2V, 3V, etc.
The results was tabulated.

Results and discussion

8 Describe what happens to the microammeter reading and the CRO trace as the capacitor is being charged up.

The microammeter reading increase momentarily, then it decrease to zero in a few second.

After the capacitor had been completely charged,the CRO trace is a horizontal line, which continuously move up.

9 Tabulate the times for the p.d. across the capacitor to reach 1 V, 2 V, 3 V, etc. as below:

Plot a graph of p.d. across the capacitor against time.

How is the p.d. related to the time?

p.d. is directly proportional to time.

11 Deduce a relationship between the charge on the capacitor and the p.d. across it.

From the graph it is found that p.d. is directly proportional to time.

Since Q=CV => V=Q/C

Therefore if V across the capacitor is directly proportional to t, Q is directly proportional to time as current was constant.

Conclusion

We can find out that the p.d. across the capacitor is directly proportional to the time needed. Given that the charging current is constant.

Sharing

The experiment is much easier than the last one , but we encountered some obstacles in connecting wires , as usual , we messed up positive and negative terminals and couldn’t conduct it smoothly. At last, we had to call for help.

Suggestion

and there may be some personal error , for example counting the time taken for the capacitor be charged to extent value was rather inaccurate. Perhaps, we could conduct the experiment several times and compute out the average value.

Reference list