An RC circuit is shown in fig.7.1. Since, in practical circuits, power is always switched on at certain time, a switch is provided here. This switch closes at time .
We are interested in finding how voltage across capacitor changes with time? We can also assume that voltage across the capacitor is zero . Using Kirchoff's voltage law across the only loop in circuit we can find the equation relating , and .
Using the characterstic equations of capacitors, resistors i.e.,
|For , constant|
|Thus, ; here is constant|
The curves showing and are shown in the figures 7.2 and 7.3.
Consider the figure shown in 7.1. The switch is closed at .
For RC circuit with source voltage zero, and an initial capacitor voltage of , this expression reduces to .
For constant current charging of a capacitor, as shown in 7.4, the analysis:
The switch is turned off at sec. There is no charge on the capacitor initially. Therefore, after and before , the circuit is equivalent to figure 7.7
Taking thevenin equivalent in the direction of the arrow leads to figure 7.8
, the switch is once again thrown open and the equivalent circuit is shown in figure 7.9
The graph of with time is shown in figure 7.10