The time constant can be derived from the discharge characteristic as well as the charging one except that the time is calculated from the time taken for Vc to fall to 36.8% of Vs. This is less easy to set up since the triggering is more difficult. It could be used with C values of the order of 1000 μF where the times are several seconds so that manual triggering could be used. The circuit to be used is changed to that shown. The capacitor is first charged by switching to the battery and then discharged using the switch in the other position.
The circuit can be adapted to small C values if the switch and battery are replaced by a square wave generator. This alternately charges and discharges the capacitor giving both characteristics. Adjust the generator frequency and the timebase controls to get the best trace.
If you have any comments or suggestions for improvements please e-mail experiments@picotech.com.
Appendix
Suppose the cell has EMF Vs and the voltages across the resistor and capacitor at any instant are Vc and Vr. As the capacitor charges, the value of Vc increases and is given by = q/C where q is the instantaneous charge on the plates. At this instant (time t) there will be a current I flowing in the circuit.
We know that current is given by the rate of change of charge. So
We also know that Vs = Vc + Vr and Vc = q/C
From Ohm’s Law we have that Vr = iR
Since Vs = Vc + Vr we get
re-arranged…
This equation can be shown to have the solution
where Q is the maximum charge i.e. C Vs .
When t = RC the equation becomes
But
i.e. the value of q is 63.2% of the maximum value of Q when t = RC