Question

The switch in the circuit of Figure 1 has been in position A for a long time. At t-0, it is moved to position B The resulting step response of the series RLC circuit is described by the r differential equation (1). Figure 1 dt L dt LC LC The solution to equation (1) has two components the transient response vt(t) and the steady state response, Vss(t) v(t)v(t)+ Vss(t) The transient response v(t) is the same as that for the source-free case for ?>a, (overdamped) for ?=a (critically damped) for ?<a, (underdamped) =c (A coso,t + A2sino,t) where ? 2L and LC The steady state response Vss(t) is the final value of v(t), i.e. Vss(t) In the frequency domain, the impedances of the inductor and capacitor are given by and Z1 =ja.

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