If the lagging power factor of a load decreases, the line losses will

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increases

Explanation: If the lagging power factor of a load decreases, the current drawn from the supply must increase to maintain the same real power. Since line losses are proportional to the square of the current ($I^2R$), an increase in load current leads to significantly higher ohmic losses in the transmission line.

Working Principle: The real power delivered to a load is given by $P = VI \cos\phi$. For a constant $P$ and $V$, if $\cos\phi$ (power factor) decreases, the current $I$ must increase. The power lost in the line is $P_{loss} = I^2 R$, where $I$ is the line current and $R$ is the line resistance. Consequently, as the current increases due to the lower power factor, the line losses increase quadratically.

Key Formulas: $P = VI \cos\phi$ — Active power relation; $P_{loss} = I^2 R$ — Ohmic line loss formula

Key Points: Line losses increase with the square of the current.; A lower power factor implies a higher reactive power demand for the same real power.; Higher currents result in greater voltage drops along the transmission line.; Power factor correction capacitors are used to mitigate these losses.

Advantages: Improved voltage regulation; Increased system capacity; Reduction in electricity billing penalties

Disadvantages: Requires installation of compensation equipment; Added maintenance for capacitor banks

Applications: Industrial power distribution; Transmission and distribution networks

Additional Info: A lagging power factor is caused by inductive loads like motors and transformers.. Option A is incorrect because current would have to decrease, which happens only if PF increases toward unity.. Option D is incorrect because line loss is strictly dependent on the load current magnitude.

Answer: B is correct — A decrease in lagging power factor increases the required current for a constant load, leading to higher $I^2R$ line losses.

Exam Tip: Always remember that in power systems, higher current is the primary enemy of efficiency; improving PF to near unity is the standard industry approach to minimize $I^2R$ losses.

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