Power Calculator in Series RLC

Table of Contents

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A calculator to calculate the average power delivered to a resistor, a capacitor and an inductor in series, as shown below, is presented.
Series RLC Circuit
The calculator gives the impedance of the series circuit as a complex numbers in standard form , its modulus and argument, the power factor and the average power.

Formula for The Average Power Delivered to a series RLC Circuit

Simple ac Circuit

The formula of the average power delivered to an impedance \( Z \) as shown in the circuit below is given by
\[ \displaystyle \quad \quad P_a = \dfrac{V_0^2}{2 |Z|} \cos \theta \]
where \( V_0 \) is the peak voltage of the source voltage \( v_ i\). \( |Z| \) is the modulus of \( Z \) and \( \theta \) its argument.
The term \( \cos \theta \) is called the power factor.

and define the following parameters used in the calculations
\( \omega = 2 \pi f \) , angular frequency in rad/s
\( X_C = 1 / (\omega C) \) , the capacitor reactance in ohms \( (\Omega) \)
\( X_L = \omega L \) , the inductor reactance in ohms \( (\Omega) \)
The formula of the impedance \( Z \) of the series RLC circuit shown above and write it in standard complex form as follows
\( Z = R + (X_L - X_C) j \)
and in polar form as follows
\[ Z = |Z| e^{j \theta} \]
The formulae for the modulus \( r \) and argument \( \theta \) are given by (see proof at the bottom of the page)

Modulus: \( |Z| = r = \sqrt {R^2 + (X_L - X_C)^2 } \) in ohms \( (\Omega) \)

Argument: \( \theta = \arctan \left(\dfrac{X_L - X_C}{R} \right) \) in radians or degrees

Use of the calculator

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

Peak Voltage \( V_0 \) = Volts

Resistance R =

Capacitance C =

Inductance L =

Frequency f =



More References and links

Power in AC Circuits
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