Question

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.

• A. $0.63I_{0}$
• B. $0.50I_{0}$
• C. $0.37I_{0}$
• D. $I_{0}$

Answer 1

Answer: (A)

$0.63I_{0}$

Answer 2

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 $I=0.63 I_{0}$