Page 249 - Basic Electrical Engineering

So, to find the value of K we will put the initial conditions, i.e., when t = 0, v c
= V

therefore, −l V = 0 + K
n
or, K = −l V
n

The eq. (v) is written as

or,

and

The time constant, τ of the circuit is the time in seconds taken for the voltage
across the charged capacitor to become zero if the initial rate of decay is

maintained as shown by the dotted line AB. OB is the time constant, τ as has
been shown.
If we calculate the value of v at t = τ, we get
c

and