A constant current of I = 15 A exists in a solenoid whose inductance is L = 42.2

Question

A constant current of I = 15 A exists in a solenoid whose inductance is L = 42.2 H. The current is then reduced to zero in a certain amount of time.

(a) If the current goes from 15 to 0 A in a time of 75 ms, what is the emf induced in the solenoid?
(b) How much electrical energy is stored in the solenoid? (Consider the initial energy stored.)
(c) At what rate P must the electrical energy be removed from the solenoid when the current is reduced to 0 A in a time of 75 ms? Note that the rate at which energy is removed is the power.

Explanation / Answer

induced emf = - L di/dt
L = 42.2 H, di = -15 A and dt = 75*10^-3 s
So emf = 8440 volt.
Electrical energy stored when 15 A current was flowing through is got using 1/2 L I^2
So U = 1/2 * 42.2 * 15^2 = 4747 J
Hence the power required = 4747 / 75*10^-3 = 63290 W

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