16) A battery is connected in series witha R = 0.34 ? resistor and an inductor,a

Question

16) A battery is connected in series witha R = 0.34 ? resistor and an inductor,as shown in the figure below. The switch is closedat t = 0. The time constant of the circuitis ? = 0.24 s, and the maximum current in thecircuit is I = 8.3 A. Find the following.

(a) the emf of the battery
V

(b) the inductance of the circuit
mH

(c) the current in the circuit after one time constant haselapsed
A

(d) the voltage across the resistor and the voltage across theinductor after one time constant has elapsed

Explanation / Answer

a) max current = V/R

V = 8.3*0.34=2.82 V

b) tau = L/R

L = tau R = 0.24*0.34= 0.0816 H = 81.6 m H

c) I = Imax ( 1 - e^(-t/tau))

I = 8.3*(1-e^(-1))= 5.25 A

d) Vrestistor = I R = 5.25*0.34= 1.79 V

Vinductor = 2.82-1.79= 1.03 V

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