Page 239 - Basic Electrical Engineering

or,

where , called the time constant of the circuit.

At time t = ∞, the current is the steady-state current. Then

The eq. (2.6) can then be expressed as i = I (1 – e (–t/τ) ).
0

This current has two components, i.e.,

i = I and I e –t/τ
0
0

I is the steady-state current and I e –t/τ is the transient component of the
0
0
current which goes on decreasing exponentially with the passage of time. The
rise in current in the R–L circuit when the switch is closed has been shown in
Fig. 2.161. The rise in current in the circuit is initially rapid but gradually the

rise becomes slower and finally comes to a steady-state value. Although
theoretically speaking, the current would reach its steady-state value after
infinite time, but practically this time is too small a time—a fraction of a

second only. The time taken by the current to reach 63.2 per cent of its final

value is called the time constant of the circuit where, .

If we put t = , the value of i will become 0.632 of I as
0

Put t = τ