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
5.1 Instantaneous power
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
The power in the AC circuit at any instant of time is known as instantaneous power.
It is equal to the product of values of alternating voltage and alternating current at that time.
Mathematically,
$${P_{ins}} = {V_{ins}}{i_{ins}}$$$${P_{ins}} = \left( {{V_0}\sin \omega t} \right)\left( {{i_0}\sin \left( {\omega t - \phi } \right)} \right)$$$${P_{ins}} = {V_0}{i_0}\sin \omega t\left[ {\sin \omega t\cos \phi - \cos \omega t\sin \phi } \right]$$$${P_{ins}} = {V_0}{i_0}\left( {{{\sin }^2}\omega t\cos \phi - \sin \omega t\cos \omega t\sin \phi } \right)$$$${P_{ins}} = {V_0}{i_0}\left( {{{\sin }^2}\omega t\cos \phi - \frac{{\sin 2\omega t}}{2}\sin \phi } \right)$$
