Question

Problem 8. Provide the voltage equation for the circuit components below in the s-domain Laplace). PLEASE NOTE: Each answer should be in the form of V(s)-where the blank is the Laplace transform of the voltage equation for each element. a) R=20Ω c) L= 5m1H with 1,-10.1 d) C 10uF with VoOV e) C-5pF with Vo -10V 772 WI

Answer 1

a) V = iR V(s) = I(s) R b) v = L di/dt - voltage across Inductor Apply L . T on both sides V(s) = LSI(s) - Li_L(0^-) = LSI(s) - LI_0 [I_0 = 0 L = 5 ml - 1] V(s) = SL I(s) - 0 V(s) = SL I(s) = 5 times 5 times 10^-3 I(s) = 5s times 10^-3 I(s) c) v = L di/dt rightarrow voltage across Inductor Apply L . T on both sides L = 5 mlt I_0 = 10A V(5) = Sl I(s) - LI_0 V(s) = s times 5 times 10^-3 I(s) - 5 times 10^-3 times 10 v(s) = 5 times 5 times 10^-3 I(S) - 0 . 05 d) c = 10 mu F with v_0 = 0 v v(t) = 1/c integral I dt rightarrow voltage across capacitor Apply Laplace on both side V(s) = 1/sc I(s) + v_0/s \r\n v(s) = 10^5/s I(s) e) c = 5 mu F, v_0 = 10v v(t) = 1/c integral I dt