# Discharging capacitor

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

### 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.