> Q. In an $L-R$ circuit, time constant is that time in which current grows from zero to the value where $ {{I}_{0}} $ is steady state current. – LIVE ANSWER TODAY

Q. In an $L-R$ circuit, time constant is that time in which current grows from zero to the value where $ {{I}_{0}} $ is steady state current.

In This post you will get answer of Q.
In an $L-R$ circuit, time constant is that time in which current grows from zero to the value where $ {{I}_{0}} $ is steady state current.

Solution:

The equation for growth of current in $L-R$ circuit is given by

$I=I_{0}left(1-e^{-t / tau}right)$

Here, $tauleft(=frac{L}{R}right)$ is called time constant of the $L-R$ circuit.

At a time equal to one time constant $i e$, at $t=tau$

$I=I_{0}left(1-e^{-1}right) $

or $I=I_{0}left(1-frac{1}{e}right)$

or $I=0.63 I_{0}$

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