Parallel RL circuit Impedance Calculator

Table of Contents

A calculator to calculate the equivalent impedance of a resistor and an inductor in parallel. The impedance is given as a complex number in standard form and polar forms.

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Formulae for Parallel R L Circuit Impedance Used in Calculator and their Units

parallel R L circuit

Let \( f \) be the frequency, in Hertz.
The angular frequency is given by
\( \omega = 2 \pi f \) , in rad/s
The inductive reactance
\( X_L = \omega L \) , in ohms \( (\Omega) \)
The impedance of the inductor \( L \) is given by
\( Z_L = j \omega L \)
Let \( Z \) be the equivalent impedance to the parallel RL circuit shown above and write it in complex form as follows
\[ \dfrac{1}{Z} = \dfrac{1}{R} + \dfrac{1}{Z_L} \]
\( Z = \dfrac{R Z_L}{R + Z_L} = \dfrac{ j R \omega L }{R+j \omega L } = \dfrac{1}{\dfrac{1}{R} - j \dfrac{1}{\omega L}} \)

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

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

Argument (Phase): \( \theta = \arctan \left( \dfrac{ R }{\omega L} \right) \) 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 =

Inductance L =

Frequency f =
Number of Decimals        

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
Engineering Mathematics with Examples and Solutions