# Power Of Alternating Current

As we know, in an alternating current circuit, both electromotive force and current change continuously with respect to time. This is the main reason why we cannot calculate the power of the same, as power is equal to the product of voltage and time. The average power of an alternating current circuit can be calculated by calculating the instantaneous power of the circuit.
In an AC circuit, the average power dissipation can be calculated by,

$$\begin{array}{l}P_{av}=\frac{\int_{0}^{T}~VI~dt}{\int_0^{T}~dt}\end{array}$$
The instantaneous e.m.f and the current in an AC circuit are given by:
$$\begin{array}{l}V = V_0~sin~\omega t\end{array}$$
$$\begin{array}{l}I = I_0~sin~(\omega t~-~\phi)\end{array}$$
In a series LCR circuit, it is shown that:
$$\begin{array}{l}P_{av} = V_{rms}~I_{rms}~cos~\phi\end{array}$$

Where, V0 and I0 are peak values of e.m.f and current.

$$\begin{array}{l}\omega = \frac{2\pi}{t}\end{array}$$

t is the period of alternating current.
Vrms Irms is called apparent power or virtual power.

$$\begin{array}{l}\phi = 0\end{array}$$
then,
$$\begin{array}{l}P_{av} = I^2{rms}~R\end{array}$$
Power dissipation takes place only in the resistor in an AC circuit.
For a series LCR circuit at resonance, a purely resistive circuit is given as:
$$\begin{array}{l}\phi = 0^{\circ}\end{array}$$
It is represented as,
$$\begin{array}{l}P_{av}\end{array}$$
$$\begin{array}{l}V_{rms}~I_{rms}\end{array}$$
For a purely inductive or capacitive circuit,
$$\begin{array}{l}\phi = 90^{\circ}\end{array}$$
$$\begin{array}{l}P_{av} = 0\end{array}$$
Power increases when an a.c. circuit contains the resistor. The power of a.c. circuit decreases when an inductor or capacitor is connected in series to the resistor.
The average power of an a.c circuit is called the true power of the electrical circuit.
Power Factor of an alternating current circuit is the ratio of true power dissipation to the apparent power dissipation in the circuit.
Also,
$$\begin{array}{l}cos~\phi = \frac{R}{Z}\end{array}$$
The value of the power of an a.c circuit lies between 0 and 1. For a purely inductive or capacitive circuit, it is 0 and for the purely resistive circuit, it is 1.
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## Frequently Asked Questions – FAQs

### Define the power factor of an alternating current circuit.

It is the ratio of true power dissipation to the apparent power dissipation in the circuit.

### What happens to the power of the AC circuit when an inductor or capacitor is connected in series to the resistor?

In this situation, the power of the AC circuit decreases.

### How is the average power dissipation calculated in an AC circuit?

It is calculated by the formula:

$$\begin{array}{l}P_{av}=\frac{\int_{0}^{T}~VI~dt}{\int_0^{T}~dt}\end{array}$$

### What is the formula to calculate the apparent power or virtual power?

$$\begin{array}{l}P_{av} = I^2{rms}~R\end{array}$$

### State true or false: Power increases when an AC circuit contains the resistor.

True.
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