A constant current of I = 15 A exists in a solenoid whose inductance is L = 36.8

Question

A constant current of I = 15 A exists in a solenoid whose inductance is L = 36.8 H. the current is then reduced to zero in a certain amount of time. If the current goes from 15 to 0 An in a time of 75 ms, what is the emf epsilon induced in the solenoid? How much electrical energy is stored in the solenoid? (Consider the initial energy stored.) At what rate P must the electrical energy be removed from the solenoid when the current is reduced to 0 An in a time of 75 ms? Note that the rate at which energy is removed is the power.

Explanation / Answer

a)Induced emf is given by:

e = -L di/dt

e = - 36.8 (0 - 15)/75 x 10^-3 = 7360 Volts

Hence, e = 7360 Volts

b)Energy stored in solenoid is given by

U = 1/2 L I^2

U = 1/2 x 36.8 x 15^2 = 4140 J

Hence, U = 4140 J

c)Power = U/t

P = 4140/75 x 10^-3 = 55200 Watts

Hence, P = 55200 Watts

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