Transmission efficiency of a transmission line increases with the _________.

Question

Examoogle · Accepted Answer

The correct answer is Option B: increase in power factor and voltage. Transmission efficiency is defined as the ratio of power received at the load end to the power sent from the sending end. Increasing the transmission voltage reduces the current for a given power, thereby lowering $I^2R$ losses, while increasing the power factor also minimizes current to deliver the same active power.

Step-by-Step Solution & Concepts:
Transmission efficiency is defined as the ratio of power received at the load end to the power sent from the sending end. Increasing the transmission voltage reduces the current for a given power, thereby lowering $I^2R$ losses, while increasing the power factor also minimizes current to deliver the same active power.

Working Principle: The transmission efficiency $\eta$ is expressed as $\eta = \frac{P_{	ext{out}}}{P_{	ext{out}} + 	ext{Losses}}$. Losses in the line are $I^2R$. Since power $P = VI \cos\phi$, the current is $I = \frac{P}{V \cos\phi}$. Substituting this into the loss equation gives $	ext{Losses} = \frac{P^2R}{V^2 \cos^2\phi}$. Clearly, increasing $V$ or $\cos\phi$ decreases line losses, thus improving efficiency.

Key Formulas: $\eta = \frac{P_r}{P_s} 	imes 100\%$ — Efficiency definition; $	ext{Losses} = I^2 R = \left(\frac{P}{V \cos\phi}ight)^2 R$ — Power loss relation

Key Points: Transmission efficiency increases as line current decreases for a fixed power transmission.; Higher voltage levels reduce the magnitude of current required for the same power delivery.; Higher power factor ensures that a greater proportion of the apparent power is useful real power.; Transmission efficiency is limited by line resistance, which is minimized by using high voltage levels.

Advantages: Lower power loss in conductors; Improved voltage regulation; Increased power transfer capability

Disadvantages: High insulation costs at increased voltages; Higher complexity in maintenance and hardware

Applications: High Voltage Direct Current (HVDC) systems; Extra High Voltage (EHV) AC transmission grids

Additional Info: For a constant load power, the line loss is inversely proportional to the square of voltage and the square of power factor.. Option A is incomplete because ignoring power factor changes fails to account for current variation.. Option C is technically incorrect as decreasing voltage/power factor increases line current, leading to higher losses.

Answer: B is correct — Transmission efficiency is directly proportional to both voltage and power factor as they collectively reduce the line current and resistive losses.

Exam Tip: Remember the inverse square relation: $I^2R$ losses reduce significantly when voltage is stepped up; this is the primary reason why we use high voltage for long-distance power transmission.

Examoogle · Answer

Option A: increase in voltage only power factor remains constant

Examoogle · Answer

Option C: decrease in power factor and voltage

Examoogle · Answer

Option D: increase in power factor but the decrease in voltage

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