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