Question

Circuit 1 Transient response of a series RLC circuit The two switches in the circuit in Figure 8 operate synchronously. When switch 1 is in position "a", switch 2 is closed. When switch 1 is in position "b", switch 2 is open. Switch 1 has been in position "a" for a very long time. At 1-0, it moves instantaneously to position 4Ω t=0 2 8Ω 100mH 150V| 2Ω 60 V Figure 8: Circuit for Tasks 3 and 4 TASK 3 Find the expression for vc(t) for t 20

Answer 1

At time t = 0^bar, circuit is in steady state condition, capacitor act as open circuit, inductor acts as short circuit at t = 0^bar i_L(0^bar) = -150/4 + 8 + 18 = -5 A V_c (0^bar) = i_L(0^bar) times 18 = -90 V. at t greaterthanorequalto 0 I = 60/s + 0.5 + 90/s/2 + 8 + 0.1 s + 500/s I = 150 + 0.5 s/0.1 s^2 + 10 s + 500 I = 5 s + 1500/s^2 + 100 s + 5 k V_c (s) = -90/s + i(500/s) V_c (s) = -90/s + 500 (5 s + 1500)/s(s^2 + 100 s + 5 k) V_c (s) = -90/s + 150/s - 150 (s + 50)/(s + 50)^2 + 50^2 - 5000/(s + 50)^2 + 50^2 V_c (t) = 60 - e^-50 t [150 cos 50 t + 100 sin 50 t] V: t greaterthanorequalto 0

Answer 2