Physics > Alternating Current > 5.0 Power in AC circuit
Alternating Current
1.0 Introduction
2.0 Alternating current and alternating voltage
2.1 Instantaneous current and voltage
2.2 Mean or average current and voltage
2.3 Root mean square current and voltage
2.4 Form factor
3.0 Some important terms
4.0 Circuit element in AC circuit
4.1 Pure resistor circuit
4.2 Pure inductor circuit
4.3 Pure capacitor circuit
4.4 Series $L-R$ circuit
4.5 Series $C-R$ circuit
4.6 Series $L-C-R$ circuit
4.7 Resonance series $L-C-R$ circuit
4.8 Quality factor
4.9 Summary
5.0 Power in AC circuit
5.4 Power factor
2.2 Mean or average current and voltage
2.3 Root mean square current and voltage
2.4 Form factor
4.2 Pure inductor circuit
4.3 Pure capacitor circuit
4.4 Series $L-R$ circuit
4.5 Series $C-R$ circuit
4.6 Series $L-C-R$ circuit
4.7 Resonance series $L-C-R$ circuit
4.8 Quality factor
4.9 Summary
It is defined as the ratio of the power to apparent power of an AC circuit.
$$\cos \phi = \frac{{{\text{True power}}}}{{{\text{Apparent power}}}}$$
Power factor is also defined as the ratio of the resistance to the impedance of an ac circuit.
From impedance triangle we can write,
$$\cos \phi = \frac{R}{Z}$$
In pure resistor circuit
$$Z = R$$
So, $$\cos \phi = 1$$ or $$\phi = 0^\circ $$
In pure inductor or capacitor circuit
$$\phi = 90^\circ $$
$$\cos \phi = 0$$
In $R-L$ circuit
$$Z = \sqrt {{R^2} + X_L^2} $$ and $$\cos \phi = \frac{R}{Z}$$
In $R-C$ circuit
$$Z = \sqrt {{R^2} + X_C^2} $$ and $$\cos \phi = \frac{R}{Z}$$
In series $L-C-R$ circuit
$$Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} $$ and $$\cos \phi = \frac{R}{Z}$$
At resonance, $${X_L} = {X_C}$$
So, $$Z = R$$$$\phi = 0^\circ $$ or $$\cos \phi = 1$$
