Electrical Engineering ⇒ Topic : Step Response of R-C Circuit

STEP RESPONSE OF R-C CIRCUIT

Figure (a) shows a series R-C circuit. The capacitance of the circuit has an initial charge q_o such that it opposes the flow of charging current. Let the switch be closed at t = O.

                    Figure (a) Series R-C circuit.

The circuit equation in time domain is given by

                           ........... (1)

The Laplace transform of Eq. (1) is given by

                 ................ (2)

In the above equation, the term i(0 -) represents the initial current of the circuit such that

Taking the inverse Laplace transform, we obtain

                                 ........... (3)