A sensitive electronic device with resistance of 175 ohms is to be connected to

Question

A sensitive electronic device with resistance of 175 ohms is to be connected to a source emf by means of a switch. The device is designed to operate with a current of 36 mA but, to avoid damage, the current must not exceed 4.9 mA in the first 58µs after the switch is closed. To protect the device, it is connected in series with an inductor, (a) What is the emf that the source must have? Suppose the internal resistance is negligible. (B) What inductance is required? And (c) What is the time constant? A sensitive electronic device with resistance of 175 ohms is to be connected to a source emf by means of a switch. The device is designed to operate with a current of 36 mA but, to avoid damage, the current must not exceed 4.9 mA in the first 58µs after the switch is closed. To protect the device, it is connected in series with an inductor, (a) What is the emf that the source must have? Suppose the internal resistance is negligible. (B) What inductance is required? And (c) What is the time constant?

Explanation / Answer

a)

R = resistance of the device = 175 ohms

i = operating current = 36 mA = 0.036 A

EMF = voltage across the device after long time = iR = 0.036 x 175 = 6.3 volts

b)

current in the circuit is given as

i(t) = I (1 - e-Rt/L)

at t = 58 x 10-6 s , i(t) = 0.0049

0.0049 = 0.036 (1 - e-175 (58 x 10-6)/L )

L = 0.0693 H

c)

T = time constant = L/R = 0.0693/175 = 0.000396

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