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# R-C Circuits

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.,

and using KVL

 for for    , For    , constant Thus,    ; here  is constant

At , capacitor voltage will be 0. Hence

Alternatively,

 at Thus,

Thus,

 (7.1)

The curves showing and are shown in the figures 7.2 and 7.3.

These show the exponetially decaying (growth) nature of current (voltage across capacitor).

Consider the figure shown in 7.1. The switch is closed at .

Now,

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:

 (7.2) (7.3)

That is, voltage varies linearly with time on constant current charging.

 0

Now consider the circuit shown in figure 7.6

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

Therefore ,

For , we have the following equation

After , the switch is once again thrown open and the equivalent circuit is shown in figure 7.9

Now,

Therefore,

The graph of with time is shown in figure 7.10

Next: Sinusoidal Steady State Response Up: Introduction to Electronics Previous: Transient response of RL   Contents
ynsingh 2007-07-25