The particular solution is obtained from the forcing

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Unformatted text preview: K 2 known, the final solution the capacitor voltage is vc (t ) Vs Vs e t RC . The solution contains two terms. The first term represents the steady‐state response and the second term represents the transient‐response. The capacitor voltage starts with zero and slowly grows to the full DC value. DC Steady State The transient terms in the expressions for voltage and current in RLC circuits decay to zero with time, except with LC circuits having R=0. For DC sources, the steady state voltage and currents will also be zero. From ic (t ) C dvc (t ) , if steady‐state capacitor voltage is constant then the steady‐state capacitor dt current will be zero as well. In other words, capacitor behaves as an open circuit. For inductance, vL (t ) L diL (t ) . As steady‐state inductor current will be constant, the voltage drop dt across the inductor will be zero. In other words, inductor behaves like a short circuit. 72 EE1002 Introduction to Circuits and Systems Thus, when obtaining steady‐state solutions of RLC circuits with DC sources, at first the capacitors are replaced by open circuits an...
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This document was uploaded on 01/20/2014.

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