RC-circuit met bron

When a DC source is applied abruptly to an RC circuit, its voltage is represented as a unit step function.

The voltage across the capacitor is the step response.

Since the voltage across a capacitor cannot change instantaneously, its value immediately after switching remains the same as the value immediately before switching.

By applying Kirchhoff's current law at a time equal to zero, rearranging the terms, and rewriting the equation for a time greater than zero, a first-order differential equation is obtained.

Integrating the equation, applying the limits, and taking the exponential on both sides yields the step response of the capacitor for times greater than zero.

Combining this with the capacitor's initial voltage as the circuit response for a time less than zero gives the complete response of the RC circuit.

In time, the capacitor's voltage increases exponentially and approaches the source's voltage.

If the capacitor is initially uncharged, the complete response gets modified accordingly. From this, the current through the capacitor is determined and is observed to be exponentially decreasing with time.