First slide

Time -Varying current in L-R circuit

Question

In the given circuit, let i₁ be the current drawn from battery at time t = 0 and i₂ be steady current at $t = \infty$ , then the ratio $\frac{i_{1}}{i_{2}}$ is

Moderate

A

1.0
B

0.8
C

1.2
D

1.5

Solution

At t = 0, inductor behaves as open circuit, so
$i_{1} = \frac{10}{10} = 1 A$
At $t = \infty$ inductor behave as short circuit, so
$i_{2} = \frac{10}{8} = \frac{5}{4} A$
Hence, $\frac{i_{1}}{i_{2}} = \frac{1}{5 / 4} = \frac{4}{5} = 0.8$

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