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.
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
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".
Results
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