# Series RC circuit Impedance Calculator

Table of Contents

\( \) \( \) \( \)
A calculator to calculate the equivalent impedance of a resistor and a capacitor in series. The calculator gives the impedance as a complex number in standard form and
polar forms.

## Formulae for Series R C Circuit Impedance Used in the Calculator and their Units

Let \( f \) be the frequency, in Hertz, of the source voltage supplying the circuit.

and define the following parameters used in the calculations

\( \omega = 2 \pi f \) , angular frequency in rad/s

\( X_C = 1 / (\omega C) \) , the capacitive reactance in ohms \( (\Omega) \)

The impedance of the capacitor \( C \) is given by

\( Z_C = \dfrac{1}{j \omega C} = -\dfrac{j}{\omega C}\)

Let \( Z \) be the equivalent impedance to the series RC circuit shown above and write it in complex form as follows

\[ Z = R + Z_C \]

\( Z = R - \dfrac{1}{\omega C} j \)

The formulae for the modulus \( |Z| \) and argument (or phase) \( \theta \) of \( Z \) are given by

Modulus: \( |Z| = \sqrt{ R^2 + \dfrac{1}{\omega^2 C^2} } \) in ohms \( (\Omega) \)

Argument (Phase): \( \theta = \arctan ( - \dfrac{1}{R \omega C} ) \) in radians or degrees

## Use of the calculator

Enter the resistance, the capacitance and the frequency as positive real numbers with the given units then press "calculate".

## Results of Calculations

## More References and links

AC Circuits Calculators

Complex Numbers - Basic Operations

Complex Numbers in Exponential Form

Complex Numbers in Polar Form

Convert a Complex Number to Polar and Exponential Forms Calculator

Engineering Mathematics with Examples and Solutions