Series RL circuit Impedance Calculator

Table of Contents

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

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

series R L 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
\( X_L = \omega L \) , the inductive reactance 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 series RL circuit shown above and write it in complex form as follows
\[ Z = R + Z_L = R + j\omega L \]
The formulae for the modulus \( |Z| \) and argument (or phase) \( \theta \) of \( Z \) are given by

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

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