# Step Response of a Series RC Circuit - Calculator

Table of Contents

An online calculator to calculate and graph the current through and voltages across a resistor, a capacitor and an inductor in series when the input a step voltage of the form \( V_0 u(t) \) where \( u(t) \) is the unit step function.

## Formulae for Voltages and Current in a series RC Circuit to a Step Input Voltage

We first give the formulas used in the series RC calculator.

The formulas developed in RC circuit response to a step voltage are presented here as they are used in the calculator.

When a voltage step function of the form \( v_i(t) = V_0 u(t) \) is the input voltage in the given cicuit, we have :

The voltage \( v_C(t) \) across the capacitor is given by

\( v_C(t) = V_0 (1 - e^{-t/RC} ) u(t) \)

The voltage \( v_R(t) \) across the resistor is given by

\( v_R (t) = V_0 e^{-t/RC} u(t) \)

The current \( i(t) \) is given by

\( i(t) = \dfrac{v_R}{R} = \dfrac{V_0}{R} e^{-t/RC} u(t) \)

\( \tau = R C \) is called the time constant of the circuit.

## Use of the calculator

Enter the source voltage \( V_0 \), the resistance \( R \), the capacitance \( C \) as positive real numbers with the given units then press "Calculate".

The time constant \( \tau \), the expressions of the voltages \( v_C(t) \) and \( v_R(t) \) and their graphs and the expression of the current \( i(t) \) are displayed.

## Results

### More References and links

series RLC circuit response to a step voltage

Engineering Mathematics with Examples and Solutions