Question

005-W19 HW-8 Due: Thur 4/11/19 312, L= 2 H. and C-118 P 9 Find the response vR(t) for t > 0 in the circuit below. Let R 16.o 60 + VR 1011(t) V ( ±

Answer 1

Using laplace Transform Z_eq = 18/s Vertical-bar Vertical-bar 2 s = 2 s (18/s)/2 s + 18/s Z_eq = 18 s/s^2 + 9 BY voltage division v_r (s) = 10/s times 3/3 + 18 s/s^2 + 9 v_R (s) = 10 (s^2 + 9)/s (s^2 + 6 s + 9) = 10 (s^2 + 9)/s (s + 3) v_R (s) = A/s + B s + c/(s + 3)^2 BY partial fraction A = 10 B = 0 C = -60 v_R (s) = 10/s - 60/(s + 3)^2 \r\n Therefore v_r (t) = 10 u (t) - 60 t e^- 3 t u (t) v_R (t) = (10 - 60 t e^- 3 t) u (t) volts (using inverse laplace transform)
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