Question

Problem 11 R3 + v(t) t=2s R2 = 20kΩ R2 R4 R5 R1 L 2mH Consider the above circuit to be in steady state before the switch closes at t- 2s. Determine the function v(t) for t> 2s and sketch the function on a relevant timescale.

Answer 1

For t_0 = 2s switch is not closed For general RL circuit i_L (t) = i_L (final) + (i_L (initial) - i_L (final)) e^-(t - t_0/T) t_0 = 2s, where switch change T = L/Req i_L (final) = steads state current for t > 2s i_L (initial) = current at t_0 = 2s (i) initial condition at t_0 = 2s inductor in steady state because connected long before rightarrow inductor short in steady state KCL at v_1 V_1 - V_2/5k + V_1/18k + V_/4k + 2mA = 0 V_1 (1/5 + 1/18 + 1/4) - V_2/5 = -2 0.5055 V_1 - 0.2 V_2 = -2 rightarrow (1) KCL at V_2 V_2 - V_1/5k + V_2/20k = 2mA -0.2 V_1 + 0.25 V_2 = 2 rightarrow (2) solving (1) & (2) V_1 = -1.1577 V, V_2 = 7.074 v therefore i_L (initial) = V_1/4k = -0.289 mA (ii) finding final current steady state for t greaterthanorequalto 2s rightarrow inductor short KCL at V_1 V_1 - V_2/5k +