Series LC circuit Impedance Calculator

Table of Contents

A calculator to calculate the equivalent impedance of an inductor and a capacitor in series. Complex numbers in standard form and polar forms are used in the calculations and the presentation of the results.

\( \) \( \) \( \)

Formulae for Series LC Circuit Impedance Used in Calculator and their Units

series LC 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
\( Z_L = j \omega L \)

\( X_C = 1 / (\omega C) \) , 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 LC circuit shown above and write it in complex form as follows
\[ Z = Z_L + Z_C = j\omega L - \dfrac{j}{\omega C} = j \left(\omega L - \dfrac{1}{\omega C} \right) \]
The formulae for the modulus \( |Z| \) and argument (or phase) \( \theta \) of \( Z \) are given by

Modulus: \( |Z| = \left| \omega L - \dfrac{1}{\omega C} \right| \)

Argument (Phase): \( \theta = \dfrac{\pi}{2} \) or \( 90^{\circ} \) if \( \omega L \gt \dfrac{1}{\omega C} \)
Argument (Phase): \( \theta = - \dfrac{\pi}{2} \) or \( - 90^{\circ} \) if \( \omega L \lt \dfrac{1}{\omega C} \)
Argument (Phase): \( \theta = 0 \) if \( \omega L = \dfrac{1}{\omega C} \)


Use of the calculator

Enter the resistance, the capacitance and the frequency as positive real numbers with the given units then press "calculate".

Inductance L =

Capacitance C =

Frequency f =
Number of Decimals        

Results of Calculations

    
    
    
    
    
    

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