Discharging capacitor

Investigation of the discharge of capacitors. Analysis techniques should include log-linear plotting leading to a determination of the time constant RC

Equipment

Method

1. Set up the apparatus as shown in the diagram.

2. Set the switch to the A position to allow the capacitor to fully charge.

3. Move the switch to the B position and start the stopwatch. Observe and record the voltage reading V at time t=0 and at 5s intervals as the capacitor discharges until about 120s have passed.

4. Repeat the experiment twice more and obtain the average V at each t.

(Note that the experiment can be repeated for different resistors or capacitors to investigate how the time constant varies with resistance and capacitance).

Graphs and calculations

1.  Calculate the natural logarithm of V at each t and tabulate this.

Plot a graph of ln(V) against t and draw a line of best fit. This should yield a straight line graph with negative gradient, showing that the decay of voltage across the capacitor is exponential. The gradient will equal -1/RC (or -1/time constant).

Where T  is the time constant of the RC circuit.

 

2.  If C is known, you can find the time constant using RC and also using the graph and check if they are the same. If C is not known, you can find it using the graph.