A battery is connected in series with a 0.28 - ? resistor and an inductor, as sh

Question

A battery is connected in series with a 0.28-? resistor and an inductor, as shown in the figure below. The switch is closed at t = 0. The time constant of the circuit is 0.18s, and the maximum current in the circuit is 8.1 A. please show work

Find the emf of the battery. V Find the inductance of the circuit. mH Find the current in the circuit after one time constant has elapsed. A Find the voltage across the resistor after one time constant has elapsed. V Find the voltage across the inductor after one time constant has elapsed.

Explanation / Answer

a) max current = V/R
V = I max R = 8.1*0.28= 2.27 V

b) tau = L/R

L = R tau = 0.28*0.18 = 0.0504 H = 50.4 mH

c) I = Imax ( 1 - e^(-t/tau)) = 8.1*(1-e^(-1))= 5.12 A

d) V = IR = 5.12*0.28= 1.43 V

e) Vinductor = 2.27 -1.43= 0.84 V

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