Establish a relation for power in an alternating current circuit. What will be the effect in the formula, when there is no reactance or resistance in the circuit? Define power factor.

Hint: We know that the source of an AC circuit is sinusoidal. Then there is a phase difference between the voltage and current. If the phase difference between the current and voltage is zero, then both are said to be in phase, and if the phase difference is not equal to zero, then both are said to be out of phase.

Formula used:
$P.F=\dfrac{R.P}{A.P}$

Complete step-by-step solution:
Power is generally used to measure work in two different contexts, one being the mechanical work and the other being electrical work.
In an AC circuit, if $R$ is the resistance when connected to say $V$ source which produces $I$ current , then the$P$ power produced in the circuit, is given as $P=I^{2}_{rms}R=\dfrac({V_{rms}}{R})^{2}R$, which is the real power. However, in an LCR combination circuit, $Z$ is the impedance of the circuit or the total resistance offered by the circuit, it is given as $Z=\sqrt{R^{2}+(X_{L}-X_{C})^{2}}$. Where, $X_{L},X_{C}$ are the inductive reactance and the capacitive reactance respectively. Then the power due to the circuit is given as $P=I^{2}_{rms}Z=\dfrac({V_{rms}}{Z})^{2}Z$ which is called the apparent power.
The power factor is defined as the ratio of real power to the apparent power in the circuit. This value varies from $0-1$.
$P.F=\dfrac{R.P}{A.P}$
If the power factor is $0$, then there is some impedance in the circuit.
If the power factor is $1$, then the circuit is said to be resistive in nature $Z=R$, and here maximum power is used to do work.
Note: The unit of power is watt, which is named after the scientist Watt. Power factor value varies from $0-1$ is only taken into account when an AC is passed through an LCR combination, like LC, LR, RC or LCR in series or parallel connection.