A battery is connected in series with a 0.27-? resistor and an inductor, as show

Question

A battery is connected in series with a 0.27-? resistor and an inductor, as shown in the figure below. The switch is closed at t = 0. The time constant of the circuit is 0.22 s, and the maximum current in the circuit is 7.6 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.
V

Explanation / Answer

a) V = iR V = .27 x 7.6 =2.052 V b) time cons = L/R =.22 L = 59.4 mH c) i = io (1- e^-1) i = i0 x .67 i= 4.824 A d)voltage = i x 4.824 = 1.30248 V e) across inductor = 2.052 - 1.30248 = .74952 V

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