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# Learning Goal: To analyze an RL circuit to determine the initial current through an inductor, the time constant, and the expression for the natural response of the inductor current, and to use the expression for the inductor current to find other circuit quantities, such as current, voltage, power, or energy. The natural response of an RL circuit is the response of the inductor current to the sudden removal of a DC source. When this occurs, the inductor releases the stored energy. Part A For the given circuit (Figure 1) , assume the make-before-break switch has been up for a long time and moves down at t=0. Find the initial current through the inductor. Assume that Is = 36.0mA , R1 = 32.0k? , R2 = 100.0k? , and L = 12.0mH . Express your answer to three significant figures and include the appropriate units. i(0?)=i(0+)= = Part C – For the original circuit, find an expression for the inductor current, i(t), for t ? 0 Enter an expression for the inductor current, i(t), for t?0. Express your answer as an algebraic expression in terms of Is, R1, R2, and L. Part D – For the original circuit, find an expression for the resistor voltage, v(t), for t ? 0+ Enter an expression for the resistor voltage, v(t), for t?0+. Express your answer as a symbolic expression in terms of Is, R1, R2, and L. Part B – Find the time constant, ?, after t = 0 The diagram (Figure 2) shows the circuit the instant after t=0. Find the time constant, ?. Assume that Is = 36.0mA , R1 = 32.0k? , R2 = 100.0k? , and L = 12.0mH . Express your answer to three significant figures and include the appropriate units.

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