Question

15. Consider the following circuit. The output Volt) is given as Ki-Ke-t/r Find τ for t > 0. 0uF t-0 3KQ 12V a) 75ms b) 100ms c) 50ms d) 150ms 16. For the problem described in question 15 find K1 fort>0. a) 6V b) 4V c) 2V d) 3V

Answer 1

At t = 0 switch is closed Apply Laplace transform Apply nodal analysis at V_0 (s) v_0 (s) - 12/s/3 k + V_0 (s) - 12/s/1/50 mu s + v_0 (s)/3 k = 0 V_0 (s) [1/3 k + s/20 k + 1/3 k] = 12/s/3 k + 12/s/20 k/s V_0 (s) [20 + 3 s + 20/60] = (12/s) 20 + 36/60 V_0 (s) = 240 + 365/s (35 + 40) v_0 (S) = 125 + 80/s (s + 40/3) v_0 (s) = 6/s + 6/s + 40/3 Apply I L T V_0 (t) = (6 + 6 e^-40/3 t) V V_0 (t) = [6 + 6 e^-t/(3/40)] V Therefore T = 3/40 sec = 75 m sec Option (a) is correct answer k_1 = 6 V option (a) is correct answer

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