Initial Conditions of capacitor

Capacitor's initial condition need to be examined before charging a capacitor. Capacitor may have some charges stored, if it has charged before but have not fully discharged. In all the examples examined in the previous sections, the capacitor was uncharged before the switch was thrown. We will now examine the effect of a charge, and therefore a voltage (V = Q/C), on the plates at the instant the switching action takes place. The voltage across the capacitor at this instant is called the initial value, as shown for the general waveform of [Fig. 1]. Once the switch is thrown, the transient phase will commence until a leveling off occurs after five time constants. This region of relatively fixed value that follows the transient response is called the steady-state region, and the resulting value is called the steady-state or final value. The steady-state value is found by simply substituting the open-circuit equivalent for the capacitor and finding the voltage across the plates. Using the transient equation developed in the previous section, an equation for the voltage $v_C$ can be written for the entire time interval of [Fig. 1]; that is, However, by multiplying through and rearranging terms: If you are required to draw the waveform for the voltage $v_C$ from the initial value to the final value, start by drawing a line at the initial and steady-state levels, and then add the transient response (sensitive to the time constant) between the two levels. The example to follow will clarify the procedure.