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

series R C circuit

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".

Resistance R =

Capacitance C =

Frequency f =
Number of Decimals        

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