First slide

Time -Varying current in L-R circuit

Question

A coil of inductance 300 mH and resistance $2 Ω$ is connected to a source of voltage 2V. The current reaches half of its steady state value in

Moderate

A

0.15 s
B

0.3 s
C

0.05 s
D

0.1 s

Solution

$i = i_{0} (1 - e^{\frac{- Rt}{L}}) \Rightarrow For i = \frac{i_{0}}{2}, t = 0 .693 \frac{L}{R}$
$\Rightarrow t = 0 .693 \times \frac{300 \times 10^{- 3}}{2} = 0 .1 s$

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