Page 248 - Basic Electrical Engineering

Thus, time constant can also be defined as the time taken in seconds for the
voltage across the capacitor to reach 63.2 per cent of its final value as has
been shown in the Fig. 2.164.

The above explanation relates to charging of the capacitor upto a voltage V
when the switch S is put in position 1. Now we will study the discharging of

the capacitor when the switch is put in position 2. The capacitor voltage now
at time t = 0 is equal to the supply voltage V. When the switch has been put

in position 2, the supply voltage is cut off and the RC circuit is short
circuited. The current flowing will be due to the voltage build up across the

capacitor. The current flowing now will be will flow in the opposite

direction to the direction when the capacitor was being charged. That is why

we have put a negative sign for i.

Again

thus

or,

or,

Integrating,

where K is the integration constant.