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Module 1. Average and effective value of sinusoida...

Module 2. Independent and dependent sources, loop ...

Module 3. Node voltage and node equations (Nodal v...

Module 4. Network theorems Thevenin’ s, Norton’ s,...

Module 5. Reciprocity and Maximum power transfer

Module 6. Star- Delta conversion solution of DC ci...

Module 7. Sinusoidal steady state response of circ...

Module 8. Instantaneous and average power, power f...

Module 9. Concept and analysis of balanced polypha...

Module 10. Laplace transform method of finding ste...

Module 11. Series and parallel resonance

Module 12. Classification of filters

Module 13. Constant-k, m-derived, terminating half...

## LESSON 18. Power factorand apparent power

**18.1 Apparent Power and Power Factor**

The power factor is useful in determining useful power (true power) transferred to a load. The highest power factor is 1, which indicates that the current to a load is in phase with the voltage across it (i.e.in the case of resistive load). When the power factor is 0, the current to a load is 90^{0 }out of phase with the voltage (i.e. in case of reactive load).

Consider the following equation

\[{P_{av}}={{{V_m}{I_m}} \over 2}\cos \theta \,W..................................................\left( {18.1} \right)\]

In terms of effective values

\[{P_{av}}={{{V_m}} \over {\sqrt 2 }}\,{{{I_m}} \over {\sqrt 2 }}\cos \theta \,\]

\[=\,{V_{eff}}\,{I_{eff}}\,\cos \,\theta \,W..................................................\left( {18.2} \right)\]

The average power is expressed in watts. It means the useful power transferred from the course to the load, which is also called true power. If we consider a dc source applied to the network, true power is given by the product of the voltage and the current. In case of sinusoidal voltage applied to the circuit, the product of voltage and current is not the true power or average power. This product is called apparent power. The apparent power is expressed in volt amperes, or simply VA.

Apparent power = V_{eff}I_{eff}

In Eq. 18.2, the average power depends on the value of cosθ; this is called the power factor of the circuit.

\[Power\,\,factor\,\left( {pf} \right)=\cos \,\theta \,={{{P_{av}}} \over {{V_{eff}}\,\,{I_{eff}}}}\]

Therefore, power factor is defined as the ratio of average power to the apparent power, whereas apparent power is the product of the effective values of the current and the voltage. Power factor is also defined as the factor with which the volt amperes are to be multiplied to get true power in the circuit.

In the case of sinusoidal sources, the power factor is the cosine of the phase angle between voltage and current

\[pf\,\, = \,\,\cos \,\,\theta\]

As the phase angle between voltage and total current increase, the power factor decreases. The smaller the power factor, the smaller the power dissipation. The power factor varies from 0 to 1. For purely resistive circuits, the phase angle between voltage and current is zero, and hence the power factor is unity. For purely reactive circuits, the phase angle between voltage and current is 90^{0}, and hence the power factor is zero. In an RC circuit, the power factor is referred to as leading power factor because the current leads the voltage. In an RL circuit, the power factor is referred to as lagging power factor because the current lags behind the voltage.