Calculate the equivalent impedance in complex and polar forms
This calculator determines the equivalent impedance of a resistor and capacitor connected in parallel in an AC circuit. The result is presented as a complex number in both standard and polar forms, giving you complete information about the impedance magnitude and phase angle.
For a parallel RC circuit, where:
The impedance of the capacitor is given by:
\(Z_C = \dfrac{1}{j\omega C} = -\dfrac{j}{\omega C}\)
The equivalent impedance \(Z\) of the parallel RC circuit is:
\(\dfrac{1}{Z} = \dfrac{1}{R} + \dfrac{1}{Z_C}\)
Which simplifies to:
\(Z = \dfrac{R Z_C}{R + Z_C} = \dfrac{R \dfrac{1}{j\omega C}}{R + \dfrac{1}{j\omega C}} = \dfrac{1}{j\omega C + \dfrac{1}{R}}\)
The magnitude (modulus) and phase angle of the impedance are:
Modulus: \(|Z| = \dfrac{1}{\sqrt{\omega^2 C^2 + \dfrac{1}{R^2}}}\) in ohms (Ω)
Phase angle: \(\theta = \arctan(-R\omega C)\) in radians or degrees
Enter the values for resistance, capacitance, and frequency to calculate the impedance: