Page 247 - Basic Electrical Engineering

This is the initial circuit current, I when the voltage across the capacitor is
o
zero. As the capacitor gets charged, current flowing through the circuit which

is, goes on decreasing from its initial value I .
0

Thus, when the circuit is switched on, while current in the circuit goes on
decreasing, the voltage across the capacitor goes on increasing as shown in

Fig. 2.164.
The time constant τ is defined as the time taken in seconds for the voltage

across the capacitor, v to attain its final value, V if the rate of rise of voltage
c
were the same as its initial value as indicated by the dotted line OC. The

initial rate of rise of voltage across the capacitor is

Figure 2.164 Transient current, i and capacitor voltage vc in a RC circuit

Now let us find out the value of the voltage across the capacitor at t = τ = RC.

Using the voltage equation