Question

I'm just starting to learn how to analyze RCL circuits so it would be great to have a step by step procedure for solving this problem. Thank you!

Problem 1 I XX For the circuit shown, determine v, i, dvldi, and dildt for t-0, v, i, dvldi, and dildt for -0', and v() and i(1) for t20. (DC) 0.25 FV Consider three cases: (a) R 5 2 (b) R-452 (c) R-1 Ω

Answer 1

Condition 1: - R = 5 ohm, t < 0 the switch is closed for a long line the behaves like an open circuit while the inductor acts like a short circuit the initial current through the inductor is i (0) = 24/5 + 1 = 4A and the initial voltage across the is the same as the voltage across the 1 ohm resistor v (0) = 1 i (0) = 4v for t > 0 the switch us opened. So that the we have the 1 ohm resistor disconnected therefore the characteristics roots are alpha = R/2 K = 5/2 times 1 = 2.5 w_0 = 1/squareroot Lc = 1/squareroot 1 times 0.25 = 2 s_1, 2 = -infinity plusminus squareroot alpha^2 - w^2_0 = -1, -4 alpha > w_0, we have therefore v (t) = v_ss + (A_1 e^-t + A_2 e^-4t) v_ss is the steads - state response \r\n therefore the final value of the voltage vf = 2Av