A battery is connected in series with a 0.31-? resistor and an inductor, as show

Question

A battery is connected in series with a 0.31-? resistor and an inductor, as shown in the figure below. The switch is closed at t = 0. The time constant of the circuit is 0.20 s, and the maximum current in the circuit is 7.7 A.
(a) Find the emf of the battery. V

(b) Find the inductance of the circuit.
mH

(c) Find the current in the circuit after one time constant has elapsed.
A

(d) Find the voltage across the resistor after one time constant has elapsed.
V

(e) Find the voltage across the inductor after one time constant has elapsed.

Explanation / Answer

Please ask if you have any doubt.I will help you.

a) The maximum current gives Vemf = (7.7A)(0.31) = 2.39V

b) Inductor value is taken from time constant = L/R

L = (0.20s)(0.31) = 62mH

c) Voltage after one time constant = 63% of max = (0.63)(2.39V) = 1.5V

d) Voltage across the inductor = 2.39 - 1.5 = 0.89V

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