Series RC circuit Impedance Calculator
Table of Contents
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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 and Solvers
Complex Numbers - Basic Operations
Complex Numbers in Exponential Form
Complex Numbers in Polar Form
Convert a Complex Number to Polar and Exponential Forms Calculator
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