# Power Calculator in Parallel 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 parallel, as shown below, is presented.

The calculator gives the impedance of the parallel 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 pallel RLC Circuit

The general 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 volatge \( v_ i\). \( |Z| \) is the modulus of \( Z \) and \( \theta \) its argument.

The term \( \cos \theta \) is called the power factor.

\( \omega = 2 \pi f \) , angular frequency in rad/s where \( f \) is the frequency of the voltage source.

The formula of the impedance \( Z \)
of the paralle RLC circuit shown above, in standard complex form, is given by

\( \dfrac{1}{Z} = \dfrac{1}{R} + j \omega \; C - j \dfrac{1}{ \omega \; L} \)

\( |Z| = \dfrac{1} { \sqrt{\dfrac{1}{R^2} + \left(\omega \; C- \dfrac{1}{\omega \; L} \right)^2 }} \)

\( \theta = - \arctan \left(\dfrac{R(\omega^2 \; L \; C - 1) }{ \omega \; L}\right) \)

and in polar form as follows

\[ Z = |Z| e^{j \theta} \]

## 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".

## Results

## More References and links

Power in AC Circuits

Formulas of Impedances 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