Question

Problem # 2 (20 points) Use Nodal Analysis and differential equation methods to find V(t) in the circuit shown and plot it for all t V(t) b 2 K 200MF 3 ov 2V Problem # 3 (20 points) Use Nodal Analysis and differential equation methods to find v(t) in the circuit shown and plot it for all t. 2n TOH 2t) 2 V

Answer 1

For t < 0 V(0^-) = 12 times 1K Ohm/3K Ohm = 4 V \r\n for t > 0: - 200 times 10^-6 d V_c/dt + V_c/1000 + V_c - 36/2000 = 0 d V_c/dt + V_c/200 times 10^-6 times 1000 + (V_c - 36)/200 times 10^-6 times 2000 = 0 d V_c/dt + 5V_c + 10/4 [V_c - 36] = 0 d V_c/dt + 5V_c + 2.5 V_c - 90 = 0 d V_c/dt + 7.5 V_c = 90 P = 7.5, Q = 90 The General solution V_c (t) = e^-pt integral Qe^+ pt dt + Ke^-Pt V_c(t) = e^-7.5t integral 90 e^+ 7.5t dt + Ke^-7.5t V_c (t) = e^-7.5t times 90 e^7.5t/7.5 + Ke^-7.5t V_c(t) = 90/7.5 + Ke^-7.5 t V_c (t) = 12 + Ke^-7.5t V_c (0) = 12 + K 4 = 12 + K K = -8 V_c (t) = 12 - 8e^-7.5t for t > 0 at t = 0^-, i(t) = 0 So V(0^-) = 2V