Question

A series LR circuit contains an emf source of 14 V having no internal resistance, a resistor, a 34 H inductor having no appreciable resistance, and a switch. If the em across the inductor is 80% of its maximum value 4.0 s after the switch is closed, what is the resistance of the resistor? A) 1.9 Ω B) 1.50 Ω C) 14 Ω D) 5.0 Ω

Answer 1

Answer:

(a) 1.9 ohm

Explanation:

We have given voltage across LR circuit $V_0=14V$

Inductance L = 34 Henry

Time t = 4 sec

It is given that emf across the inductor is 80% of maximum value in 4 sec

The voltage across RL circuit is given by

$V=V_0e^\frac{-t}{\tau }$ , here $\tau$ is time constant which is $\frac{L}{R}$ for RL circuit

Now according to question

$14\times 0.8=14e^{\frac{-4}{\tau }}$

$\tau =17.9sec$

We know that $\tau =\frac{L}{R}$

$17.9=\frac{34}{R}$

R = 1.9 ohm

So option (a) is correct