A sensitive electronic device of resistance 175is to be connected to a source of emf by a switch. The device is designed to operate with a current of 36 mA , but to avoid damage to the device, the current can rise to no more than 4.9 mA in the first 58 sec. after the switch is closed. To protect the device it is connected in series with an inductorWhat is the time constant ?

he emf of the source is 0.864, inductance L = 7 x 10^-2 H and time constant is t = 4 x 10^-4 s
Explanation:

P = 175 Ω
io = 36 x 10^-3 A
V = io R = 6.3 V
i = io ( 1 - e^-t/z)
4.9 = 36 ( 1 - e^-t/z)

e^-t/z = 1 - 4.9 / 36 = 0.864

t / tL = 0.146 => t / L/R = 0.146

L = Rt / 0.146

L = 175 x 5.8 x 10^-6 / 0.146

L = 7 x 10^-2 H

tL = 7 x 10^-2 H / 175 = 4 x 10^-4 s

Hence the emf of the source is 0.864, inductance L = 7 x 10^-2 H and time constant is t = 4 x 10^-4 s