I got A and B, just need C A 1.7 H inductor in an RL circuit (with resistance 1.

Question

I got A and B, just need C

A 1.7 H inductor in an RL circuit (with resistance 1.85 Ohm) is initially fully charged. A switch is then thrown (between positions 1 and 2, see figure), which causes the inductor to discharge. The initial current through this discharging circuit is 4.75 A. Randomized Variables I = 4.75 A L = 1.7 H R = 1.85 Ohm What is the initial energy in the inductor in J? How long will it take the current to decline to 25.00% of its initial value? Express this value in seconds. Calculate the average power dissipated in W.

Explanation / Answer

Energy stored in an inductor is E
for discharge of this energy the current in time dependent format is given by
I = Ioe^(-tR/L)
Given Io = 4.75 A
R = 1.85 ohm
L = 1.7 H

now at time t, current in circuit, I = 4.75*e^(-1.85t/1.7) = 4.75*e^(-1.088t)
power dissipated in the resistor at time t, dP = I^2R = 22.5652*e^(-2.176t)*1.85 = 41.7475*e^(-2.176t)

average power dissipated in time t = [integrate][41.7475*e^(-2.176t) dt]/t = 41.7475*[1 - e^(-2.176t)]/2.176t
as t approaches infinity
Pav = 19.184 W

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