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# Problem: In the circuit, switch S is opened at t = 0 after having been closed for a long time,(a) How much energy is stored in the inductor t = 0?(b) What is the instantaneous rate of change of the inductor’s energy at t = 0?(c) What is the average rate of change of the inductor’s energy between t = 0.0 and t = 1.0 s?(d) How long does it take for the current in the inductor to reach 0.0010 times its initial value?

###### FREE Expert Solution

The energy stored in an inductor is found by the formula:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{L}}{{\mathbf{i}}}^{{\mathbf{2}}}}$, where L is the inductor and i is the maximum current flowing in the inductor.

Power:

$\overline{){\mathbf{P}}{\mathbf{=}}{\mathbf{i}}{\mathbf{\epsilon }}}$, where i is current at t = 0 and ε is the voltage drop across the resistor.

(a)

The maximum current flowing in the inductor is given by:

i = V/R

The source voltage, ε = 6.0V

R = 12Ω at t = 0 s

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###### Problem Details

In the circuit, switch S is opened at t = 0 after having been closed for a long time,

(a) How much energy is stored in the inductor t = 0?
(b) What is the instantaneous rate of change of the inductor’s energy at t = 0?
(c) What is the average rate of change of the inductor’s energy between t = 0.0 and t = 1.0 s?
(d) How long does it take for the current in the inductor to reach 0.0010 times its initial value?