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

Question

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

Examoogle · Accepted Answer

Option C: Be 0.707 leading

Explanation & Concepts:
Voltage regulation of a transmission line is defined as the change in receiving-end voltage from no-load to full-load. For a short transmission line, when the resistance ($R$) equals the inductive reactance ($X$), zero regulation occurs if the load power factor is capacitive (leading) such that the voltage drop across the impedance is exactly compensated by the phase shift.

Working Principle: The approximate voltage regulation formula is given by: $	ext{Regulation} \approx \frac{I(R \cos \phi + X \sin \phi)}{V_r} 	imes 100\%$. For the regulation to be zero, the numerator must be zero, implying $R \cos \phi + X \sin \phi = 0$. Given $R = X$, this simplifies to $\cos \phi + \sin \phi = 0$, which yields $	an \phi = -1$, corresponding to a power factor angle of $-45^{\circ}$ (leading). The power factor is $\cos(-45^{\circ}) = 0.707$ leading.

Key Formulas: $	ext{Regulation} \approx \frac{I(R \cos \phi + X \sin \phi)}{V_r}$ — Approximate voltage regulation formula for short transmission lines; $	an \phi = -\frac{R}{X}$ — Condition for zero voltage regulation

Key Points: Voltage regulation is zero when the load power factor is leading.; For $R=X$, the required leading power factor is $0.707$.; A negative power factor angle signifies a capacitive load.; Short transmission lines are modeled as a series impedance $Z = R + jX$.

Advantages: Minimizes voltage variation at the receiving end.; Improves system stability when operating near zero regulation.

Disadvantages: Requires significant capacitive compensation.; Applicable only to specific R/X ratios.

Applications: Transmission line design; Reactive power compensation studies

Additional Info: Option A (unity) results in positive regulation due to the resistive drop.. Option B (zero pf) would lead to extreme voltage drops.. The value $0.707$ is $\frac{1}{\sqrt{2}}$, typical for $45^{\circ}$ phase shifts.

Answer: C is correct — The zero regulation condition with $R=X$ requires a leading power factor of $\cos(45^{\circ}) = 0.707$.

Exam Tip: Always remember that inductive loads (lagging) cause voltage drops, while capacitive loads (leading) cause voltage rises; zero regulation is the point of exact balance.

Examoogle · Answer

Option A: Have unity power factor

Examoogle · Answer

Option B: Have zero power factor

Examoogle · Answer

Option D: Be 0.707 lagging

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)