A 24-V battery is connected in series with a resistor and an inductor, with R =

Question

A 24-V battery is connected in series with a resistor and an inductor, with R = 9.4 Ohm, and L = 4.8 H, respectively, Find the energy stored in the inductor when the current reaches its maximum value. Apply the expression for the energy stored in an inductor in terms of its inductance and the current through it. J Find the energy stored in the inductor one time constant after the switch is closed. Find what fraction of current has been attained in one time constant after the circuit is closed and Use it to find the energy stored in the inductor at that point. J

Explanation / Answer

(a) Maximum current occurs at steady state,

V = IR

I = 24/9.4 = 2.553 A

Energy stored = (1/2) LI2 = (1/2)*4.8*(2.553)2 = 15.64 J

(b) At any time t,Current is given by

I(t) = Imax(1-e-t/time constant)

I(t) = 2.553(1- e-t/time constant)

At t = 1 time constant,

I(t) = 2.553(1- e-1)

I = 1.614 A

Energy stored = (1/2)LI2 = (1/2)*4.8*(1.614)2 = 6.25 J

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