Question

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In the given figure, calculate the power absorbed by the inductor at t-0 and t-1s if vs- 7uto V 1 2 2F 0.5 H 102 The power absorbed by the inductor at t-O isw The power absorbed by the inductor at t 1s isw

Answer 1

Apply KCL at mode v(s)/10 + v(s)/1/2s + v(s)/s/2 + v(s) - 7/s/7 = 0 v(1/10 + 2s + 2/s + 1) = 7/s v(s) [20s^2 + s + 20 + 10s/10s] = 7/s v(s) = 70/20s^2 + 11s + 20 current Across induction G(s) = v(s)/s/2 G'(s) = 140/s(20s^2 + 11s + 20) G'(s) = 7/s(s^2 + 0.55s + 1) G'(s) = 7/s - 7(s + 0.55)/(s^2 + 0.55s + 1) = 7/s - 7[s + 0.275/(s + 0.275)^2 + (0.96)^2 + 0.275/(s + 0.275)^2 + (0.96)^2 taking inverse Laplace L'(t) = 7 - 7[e^- 0.27t cos (0.96t) + 0.286e^- 0.27t sin(0.96t)]-(1) from equation (1) at t = 0 L_2(0) = 7 - 7