# Series RL circuit Impedance Calculator

  

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

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 = 50 mΩ Ω KΩ MΩ Inductance L = 20 μH mH H Frequency f = 1.5 GHz MHz kH Hz mHz Number of Decimals 4

## 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