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Power Factor | Power Factor Formula | What Is Power Factor

Power Factor | Power Factor Formula | What Is Power Factor :- In an alternating circuit, the ratio of real power (average power, P_avg.) to apparent power is called the power factor. We know that in an alternating circuit, the average power,

$\displaystyle {{P}_{avg.}}={{E}_{rms}}{{I}_{rms}}cos\phi$

Therefore

$\displaystyle cos\phi =\frac{{{P}_{avg.}}}{{{E}_{rms}}{{I}_{rms}}}=\frac{True\text{ }Power({{P}_{avg.}})}{Apparent\text{ }Power\left( {{P}_{app.}} \right)}$ …..(1)

Where

True Power = P_avg.

Apparent Power = E_rmsI_rms = P_app.

From the impedance triangle,

$\displaystyle cos\phi =\frac{R}{Z}=\frac{R}{\sqrt{{{R}^{2}}+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}}}}=\frac{Resistance}{Impedance}$ …..(2)

Thus, the power factor is equal to the ratio of the circuit’s resistance (R) to its impedance (Z).

Note :-

(1). For a circuit with a pure resistor or for a series LCR circuit at resonance (X_L = X_C),

$\displaystyle \phi ={{0}^{\circ }}$

$\displaystyle cos\phi =+1$

This is the maximum value of the power factor. Therefore, in a circuit with a pure resistor or in an AC circuit at resonance, the maximum power is dissipated.

(2). For a pure inductor or a pure capacitor,

$\displaystyle \phi ={{90}^{\circ }}$

$\displaystyle cos\phi =\text{0}$

This is the minimum value of the power factor. Hence, in a pure inductor or a pure capacitor, no electrical power is consumed. The current flowing through a pure inductor or a pure capacitor does not consume electrical power. This current is called reactive current or wattless current.

Next Topic :- Wattless Current | What Is Wattless Current

Previous Topic :- Average Power In LCR Circuit | Average Power In LCR Circuit Derivation Class 12

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Power Factor | Power Factor Formula | What Is Power Factor

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