Question

I need some help with this Circuit question. Please show the full steps.

Thank you.

8.17 In the circuit of Fig. 8.71, the switch instantaneously 0. Find v(t) for all moves from position A to B at t t2 0. 0.25 H 5 A 0.04Fv (t) 10Ω 4Ω Figure 8.71 For Prob. 8.17.

Answer 1

Given circuit Finding Initial voltage across capacitor v(0) and Initial current through inductor i(0): - At t < 0 the switch is closed (position - A) At t < 0 as source is DC inductor act as short and capacitor act as open circuit v_c(0) = 5(4) = 20 volts i(0) = 0 Amps (since open circuit) \r\n At t > 0 switch moved to position - B The circuit becomes as below The capacitor with initial voltage v(0) in Laplace domain can be represented as below Applying Laplace to figure-1: - writing mesh equation to above circuit \r\n I(s) (0.25s) + 20/s + I(s) (25/s) + 10 I(s) = 0 I(s) [0.25s + 25/s + 10] = -20/s I(s) [0.25s^2 + 25 + 10s]/s = -20/s I(s) [0.25] [s^2 + 100 + 40s] = -20 I(s) = -80/s^2 + 40s + 100 = -80/(s + 37.32) (s + 2.67949) v(s) = I(s) 1/sc + v(0)/s = 25/s[-80/(s + 37.32) (s + 2.67949)]