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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.
Rajasthan PMTRajasthan PMT 2007Alternating 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, $\tau\left(=\frac{L}{R}\right)$ 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 $I=0.63 I_{0}$