Question

For circuits used for transporting electric power, a low power factor implies large power loss transmission. Explain?

Answer 1

Hint: We know that a power factor is a cosine of the phase angle between the voltage and current flowing through the AC circuit. Here, we will use the formula of power in a series LCR circuit in case of alternating current. In an AC circuit, power factor is defined as the ratio of real power that is used for doing work to the apparent power that will be supplied to the circuit.

Formula used:
The formula used for calculating the power factor is given below;
$P = {V_{rms}}{I_{rms}}\cos \phi $
Here, $P$ is the power in an AC circuit, ${V_{rms}}$ is the peak value of the voltage, ${I_{rms}}$ is the peak value of current and $\phi $ is the angle between the voltage and the current.

Complete step by step answer:
Power factor is defined as the ratio of real power that is used for doing work to the apparent power that will be supplied to the circuit. Also, power factor is a cosine of the phase angle between the voltage and current flowing through the AC circuit. Therefore, for the formula used for calculating the power factor for circuits used for transporting electric power is given below;
$P = {V_{rms}}{I_{rms}}\cos \phi $
$ \Rightarrow \,\cos \phi = \dfrac{P}{{{V_{rms}}{I_{rms}}}}$
Therefore, from the above relation we can say that the power factor is inversely proportional to the current in the circuit.

Therefore, a low power factor will imply a large power loss in the circuit.

Note:We know that the power factor is inversely proportional to the current in the circuit. Therefore, when the current in the circuit will increase and the power factor will decrease. On the other hand, when the current in the circuit will decrease and the power factor will increase.