11.2 ZERO-INPUT RESPONSE OF RC CIRCUIT
The differential equations derived above can be used to solve for vC(t) for all t provided the input source function is known for all t. However, we do not know the input source function for all t. The input source function is usually known only for t > 0. It may also contain a discontinuity at t = 0. The input source function is generally unknown for t < 0.
Therefore, the effect of all the unknown currents which went through the capacitor from infinite past to t = 0– is given in a condensed manner in the form of an initial value specification for vC(t) at t = 0–. Let us denote this value as V0. Now, we can obtain the total response of the circuit by adding the two response components — zero-input response ...
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