If in a line, resistance and reactance are found to be equal and regulation is zero, then load will be

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Option C: 0.707 (lead) power factor

Explanation & Concepts:
The voltage regulation of a short transmission line is defined as the difference between the receiving end voltage at no-load and full-load, expressed as a percentage of the full-load receiving end voltage. For zero regulation, the capacitive (leading) reactive drop must exactly compensate for the resistive and inductive drops in the line.

Working Principle: The approximate formula for voltage regulation is $V_{reg} = I(R \cos \phi \pm X \sin \phi)$. Setting $V_{reg} = 0$ implies $R \cos \phi = -X \sin \phi$, which leads to $	an \phi = -R/X$. Given $R = X$, we get $	an \phi = -1$, implying $\phi = -45^\circ$. The power factor is $\cos(-45^\circ) = 1/\sqrt{2} \approx 0.707$ leading.

Key Formulas: $V_{reg} \approx I(R \cos \phi \pm X \sin \phi)$ — Approximate voltage regulation formula; $	an \phi = -\frac{R}{X}$ — Condition for zero regulation when $R=X$

Key Points: Voltage regulation is positive for lagging power factor loads.; Voltage regulation is zero at a specific leading power factor determined by $R/X$ ratio.; Voltage regulation is negative (receiving end voltage > sending end voltage) for leading power factors greater than the zero-regulation point.; For $R=X$, the load must be $0.707$ leading to maintain zero regulation.

Advantages: Maintains constant voltage at the load end.; Indicates optimal compensation requirements.

Disadvantages: Requires active power factor correction for varying loads.; Limited to specific line parameters.

Applications: Power system stability analysis.; Transmission line performance optimization.

Additional Info: The factor 0.707 is the decimal equivalent of $1/\sqrt{2}$.. Option B (Zero pf) would result in high leading voltage regulation if the line is purely capacitive.. Option D is the lag counterpart, which would result in maximum positive voltage regulation for these line parameters.

Answer: C is correct — When $R=X$ and regulation is zero, the load power factor must be $0.707$ leading to satisfy the condition $	an \phi = -R/X$.

Exam Tip: Always remember that for $R=X$, the regulation becomes zero when $\phi = -45^\circ$ (leading power factor), and it becomes negative when the power factor leads even more.

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Option A: Unity power factor

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Option B: Zero power factor

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Option D: 0.707 (lag) power factor

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