A series LR circuit includes a 9.0 V battery,a resistance of 0.20 $\Omega$,and an inductor.When the switch is closed,the circuit exhibits a time constant of 200 ms.What is the inductance of the circuit?
A) 42 mH
B) 15 mH
C) 32 mH
D) 40 mH
E) 22 mH

Question

Quizplus · Accepted Answer

The time constant $\tau$ for an LR circuit is given by $\tau = \frac{L}{R}$. Given $\tau = 200 \text{ ms} = 0.2 \text{ s}$ and $R = 0.20 \, \Omega$, we can solve for $L$: $L = \tau \times R = 0.2 \times 0.20 = 0.04 \, \text{H} = 40 \, \text{mH}$.

A Series LR Circuit Includes a 9 Ω\OmegaΩ ,And an Inductor

A Series LR Circuit Includes a 9 $\Omega$ ,And an Inductor