The efficiency of a transmission line is _____.

Question

Examoogle · Accepted Answer

The correct answer is Option A: increased with increase in load p.f.. The efficiency of a transmission line is defined as the ratio of power delivered at the receiving end to the power sent from the sending end. As the load power factor (p.f.) increases towards unity, the line current required to deliver the same amount of real power decreases, leading to reduced $I^2R$ losses and higher efficiency.

Step-by-Step Solution & Concepts:
The efficiency of a transmission line is defined as the ratio of power delivered at the receiving end to the power sent from the sending end. As the load power factor (p.f.) increases towards unity, the line current required to deliver the same amount of real power decreases, leading to reduced $I^2R$ losses and higher efficiency.

Working Principle: The transmission line efficiency is given by $\eta = \frac{P_R}{P_R + 	ext{Losses}}$. The losses in the line are dominated by $I^2R$, where $I$ is the line current. For a constant real power $P_R$ at voltage $V_R$, the current is $I = \frac{P_R}{V_R \cdot \cos \phi}$. As the power factor $\cos \phi$ increases, $I$ decreases, thereby reducing $I^2R$ losses and improving the efficiency.

Key Formulas: $\eta = \frac{P_R}{P_R + 3I^2R} 	imes 100\%$ — Efficiency calculation; $I = \frac{P_R}{V_R \cdot \cos \phi}$ — Current relationship with power factor

Key Points: Transmission line efficiency increases as the load power factor approaches 1.0 (unity).; Lower power factor requires higher current for the same real power transfer, causing higher copper losses.; Inductive loads (lagging p.f.) decrease efficiency compared to resistive loads.

Advantages: Reduced copper losses; Improved voltage regulation

Disadvantages: Low power factor increases line current leading to higher heating; Increased voltage drop at low power factor

Applications: Power system planning; Transmission line conductor sizing

Additional Info: Unity power factor ($\cos \phi = 1$) provides the minimum possible current for a given real power load.. Option B is incorrect because efficiency depends heavily on the current magnitude, which is a function of the power factor.. Option C and D are incorrect as they imply an inverse relationship which contradicts the $I^2R$ loss mechanism.

Answer: A is correct — The efficiency of a transmission line is increased with increase in load p.f.

Exam Tip: Always remember: higher power factor means lower current, which directly minimizes line losses and improves overall transmission efficiency.

Examoogle · Answer

Option B: independent of load p.f.

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Option C: increased with decrease in load p.f

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Option D: decreased with increase in load p.f.

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