First slide

Time -Varying current in L-R circuit

Question

An ideal coil of 10 H is connected in series with a resistance of 5 $Ω$ and a battery of 5V. 2 second after the connection is made, the current flowing in ampere in the circuit is

Easy

A

e^-1
B

(1-e^-1)
C

(1-e)
D

e

Solution

We know that $i = i_{max} (1 - e^{- t / τ})$
$Here τ = \frac{L}{R} = \frac{10}{5} = 2 \sec . So, at t = 2 \sec . and i_{max} = \frac{V}{R} = \frac{5}{5} = 1 we get i = 1 (1 - e^{- 2 / 2}) = (1 - e^{- 1})$

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