# Question #388 A cell produced a potential difference of 100 mV across a 20 kOhm resistor. A capacitor was then quickly inserted in series with the resistor and the potential difference across the resistor varied as shown below. What was the capacitance of the capacitor? The trace shows how the potential difference between the capacitor plates varies with time as it charges. The charging of a capacitor is an exponential process with the equation where Vt is the potential difference between the capacitor plates at time t, Vf is the final potential difference and tau is the time constant)

It can be seen that the time constant for the charging of a capacitor is the time taken for it to charge to (1 - 1/e) x, approximately 63%, of the final value.

Here the final value appears to be around 80 mV. 0.63 x 80 = 50 mV. It takes around 0.7 s for the capacitor to charge to this potential difference, i.e. tau = 0.7 s.

We are told that there is a 20 kOhm resistor in the circuit. Time constant = R x C, so C = 0.7 / 20000 = 35 microF.