If in a short transmission line, resistance and inductive reactance are found to be equal and regulation appea

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If in a short transmission line, resistance and inductive reactance are found to be equal and regulation appears to be zero then load will

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Option C: Be $0.707$ (lead)

Explanation & Concepts:
Voltage regulation of a short transmission line is defined as the change in receiving-end voltage from no-load to full-load expressed as a percentage of the full-load receiving-end voltage. For zero regulation to occur, the receiving-end voltage at no-load must be equal to the receiving-end voltage at full-load, which requires the load power factor to be leading.

Working Principle: In a short transmission line, the voltage drop is approximated by $\Delta V \approx I(R \cos \phi + X \sin \phi)$. For zero regulation, the total voltage drop must be zero, meaning $R \cos \phi = -X \sin \phi$. Given the resistance $R$ is equal to the inductive reactance $X$, we have $\cos \phi = -\sin \phi$, which implies $	an \phi = -1$. This corresponds to a leading power factor angle of $45^\circ$, resulting in a power factor of $\cos(45^\circ) = 0.707$ leading.

Key Formulas: $\Delta V = I(R \cos \phi + X \sin \phi)$ — Approximate voltage drop in a short transmission line; $	ext{Regulation} = \frac{V_{NL} - V_{FL}}{V_{FL}} 	imes 100\%$ — Percentage voltage regulation formula

Key Points: Zero voltage regulation occurs only when the transmission line supplies a leading power factor load.; For $R = X$, the phase angle must be $-45^\circ$ to perfectly compensate for the inductive voltage drop with the capacitor/leading load effect.; Inductive reactance causes lagging voltage drop, while capacitive current causes a rise in voltage at the receiving end.

Advantages: Improved receiving end voltage profile; Reduction in transmission line losses for specific load conditions

Disadvantages: Requires reactive power compensation (e.g., capacitor banks); Limited to specific load power factors

Applications: Power system stability improvement; Reactive power compensation in distribution networks

Additional Info: When the power factor is lagging, the regulation is always positive.. When the power factor is unity, the regulation is positive and determined by the resistance $R$.. Option D is incorrect as lagging power factors always lead to a voltage drop (positive regulation) in inductive lines.

Answer: C is correct — For zero regulation in a line where $R=X$, the load must have a leading power factor of $0.707$ to offset the voltage drop.

Exam Tip: Always remember that for inductive lines, a leading power factor load is required to achieve zero or negative voltage regulation.

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Option A: Have unity power factor

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Option B: Have zero power factor

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Option D: Be $0.707$ (lag)

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