In an $LR$-circuit time constant is that time in which current grows from zero to the value (where $I_{0}$ is the steady state current)

Question

Dr. Abubacker · Accepted Answer

(a) Current at any instant of time $t$ after closing an $L$-$R$ circuit is given by $I = I_{0}\left\lbrack 1 - e^{\frac{- R}{L}t} ightbrack$
Time constant $t = \frac{L}{R}$
$	herefore I = I_{0}\left\lbrack 1 - e^{\frac{- R}{L} 	imes \frac{L}{R}} ightbrack = I_{0}\left( 1 - e^{- 1} ight) = I_{0}\left( 1 - \frac{1}{e} ight)$
$= I_{0}\left( 1 - \frac{1}{2.718} ight) = 0.63I_{0} = 63\%$ of $I_{0}$

Q. In an $LR$-circuit time constant is that time in which current grows from zero to the value (where $I_{0}$ is the steady state current)

Explanation

Reviewed by Dr. Abubacker

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