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A sensitive electronic device of resistance 175 is 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 inductor What is the time constant ?


A sensitive electronic device of resistance 175 is 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 inductor

 What is the time constant ?


Grade:11

1 Answers

ROSHAN MUJEEB
askIITians Faculty 829 Points
2 years ago
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


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