Question

Figure 7.40 An RC circuit with voltage step input.

How do I use Complete Response = Transient Response + Steady State Response and Complete Response = Natural Response + Forced Response for a Step Response RC Circuit.

How do I use KVL and Mesh Analysis for a Step Response RL Circuit.

Answer 1

at t = 0^+ Capacitor shorts at t = infinity: steady state V(t) = V(infinity) + [V(0) - V(infinity)] e^- t/tau rightarrow V(t) = V_S u(t) - V_S u (+) e^- t/RC [tau = RC Time constant] V(t) = V_s u (t) [1 - e^- t/RC] \r\n Apply Laplace Transform to the Ckt Kvl on loop Time Constant tau = L/R i = V_s/S/R + LS V(S) = i(S) times LS = V_s/S (R + LS) times LS V(s) = L'/R + LS = V_s/S + R/L Apply Inverse Laplace Transform V(t) = e^- R/L t = e^- t/T V_s u(t) V_(t) = e^- R/L t u (t)