Question

2π Pulse wave: o-T fb) f-32 20

Answer 1

Laplace transform for periodic function is, L.T [v_s(t)] = 1/1 - e^-sT.LT {v_si (t)} rightarrow (I) rightarrow Laplace transform of signal in one period where t rightarrow period of the function. v_s1(t) = 10 for 0 < t < 2.5 sec = 0 for 2.5 < t < 10 sec v_s1 (s) = 10/s for 0 < t < 2 squareroot 5 = 0 for 2.5 < t < 10 sec v_s(s) = 1/1 - e^-10 s times 10/s (therefore (I)) \r\n v_c(s) = 10/sp[1 - e^-10s] 1/1 + s RC = 10/s[1 - e^-10 s] times 1/1 + s times 1.5 v_c(s) = 10/s[1 + 1.55] times 1/1 - e^-10.5 output of the given circuit v_c(t) = V_s(t) - V_R(t) v_s(t) = a_0 + sigma_n = 1^infinity cos (n w_0 t) + b_n sin (n w_0 t)} implies a_0 = area of signal in one period/period of signal = 10 times 2.5/10 a_0 = 2.5 \r\n implies a_n = 2/T integral_0^10 v_s(t). cos(n w_0 t) dt