First slide

Time -Varying current in L-R circuit

Question

In an LR circuit, time constant is that time in which current grows from zero to the value (where I₀ is the steady state current)

Easy

A

0.63 I₀
B

0.50 I₀
C

0.37 I₀
D

I₀

Solution

Current at any instant of time t after closing an L-R circuit is given by $I = I_{0} [I - e^{- \frac{R}{L} t}]$
Time constant, $t = \frac{L}{R}$
$∴ I = I_{0} [I_{0} - e^{\frac{- R}{L} \times \frac{L}{R}}] = I_{0} (1 - e^{- 1}) = I_{0} (1 - \frac{1}{e})$
$= I_{0} (1 - \frac{1}{2.718}) = 0.63 I_{0} = 63 % of I_{0}$

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