A constant current of I = 15 A exists in a solenoid whose inductance is L = 38.9

Question

A constant current of I = 15 A exists in a solenoid whose inductance is L = 38.9 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 e m f induced in the solenoid? e m f = (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.

Explanation / Answer

induced emf = - L di/dt

L =38.9 H. H, di = -15 A and dt = 75*10^-3 s

so induced emf = -38.9 * (-15) / (75*10^-3) = 7780 V

Electrical energy stored when 15 A current was flowing through is got using 1/2 L I^2

= 0.5 *38.9*15^2 =4376.25 J

the rate at which energy is removed is the power. = 4376.25 J / (75*10^-3) = 58.35 kW

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