Power is defined as the amount of work done per unit of time. In an alternating current circuit, power is given by the product of voltage and current. However, values of voltage and current change every instant in an AC circuit. Therefore, the power in an AC circuit at any instant of time is calculated by the product of instantaneous current (I) and voltage (E).
Average Power Associated with Resistance Or Non-Inductive Circuit
In a pure resistance, the alternating current developed is in phase with the alternating voltage applied.
Hence average power over a complete cycle of AC through the resistor is the product of virtual voltage and virtual current.
Average Power Associated With an Inductor
When a source of AC is connected with inductor L, the current in it grows from zero to maximum steady value I0. An induced emf develops in the inductor, which opposes the growth of current.
current is returned back to the source during the fall of current.
Thus net power given by the source in one complete cycle is zero.
Hence, work done in one complete cycle is-
Therefore, the average power over a complete cycle of an ideal inductor is zero. In fact, whatever energy is needed in building-up current in inductor L is returned back after one cycle.
Average power associated with a capacitor
When a source of AC is connected to a capacitor of capacitance C, the charge on it grows from zero to maximum steady value Qo. A definite amount of work is done in charging the capacitor, which is stored in the capacitor in the form of an electrostatic charge.
Where V0 is the maximum potential difference across the plates of the capacitor.
Energy drawn from the source during the charging of a capacitor is returned back to the source during discharging of the capacitor. This makes the net energy supplied by the source over a complete cycle zero.
Mathematically, if alternating voltage applied is-
Therefore, the average power supplied to an ideal capacitor by the source over a complete cycle of AC is also zero. In fact, whatever energy is needed in building up the voltage across the capacitor is returned back to the source during discharging of the capacitor.
Average Power in LCR Circuit or Inductive Circuit
Let the alternating emf applied to an LCR circuit be-
Hence, the average power associated in one complete cycle is the product of virtual emf virtual current and cosine of the phase angle between the voltage and current.
Power Factor Associated with an AC Circuit
∴ Power factor=cos=cos 90°=0°
Properties of AC circuits
- Automatic current can be transmitted over long distances during step-up transformers. The loss of energy is negligible.
- AC voltages can be changed using transformers.
- AC is very easily converted to DC.
- AC generators are usually more robust, and their efficiency is high.
Conclusion
This article explains the power in an AC circuit. Power is defined as the amount of work done per unit of time. In an alternating current circuit, power is given by the product of voltage and current. The circuit that has alternating sources is called an AC Circuit. In an AC circuit, the magnitude and the direction of current and voltages change at a regular interval of time.