A constant current of I = 15 A exists in a solenoid whose inductance is L = 44.7

Question

A constant current of I = 15 A exists in a solenoid whose inductance is L = 44.7 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.) E =

(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. P =

Explanation / Answer

a)induced emf = - L di/dt
L = 44.7 H, di = -15 A and dt = 75*10^-3 s
So emf = 8940 volt.
b)Electrical energy stored when 15 A current was flowing through is got using 1/2 L I^2
So U = 1/2 * 44.7 * 15^2 = 5028.75 J
c) Hence the power required = 5028.75 J /75*10^-3 = 67050 W

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