Select the correct statement for a medium overhead transmission line.

Question

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The correct answer is Option C: Load current is inversely proportional to the load power factor.. In an electrical power system, the power transferred is defined by the product of voltage, current, and the power factor. For a constant real power load, the load current is inversely proportional to the load power factor.

Step-by-Step Solution & Concepts:
In an electrical power system, the power transferred is defined by the product of voltage, current, and the power factor. For a constant real power load, the load current is inversely proportional to the load power factor.

Working Principle: The real power delivered to a load is given by $P = VI \cos(\phi)$, where $V$ is the voltage, $I$ is the load current, and $\cos(\phi)$ is the power factor. Rearranging this expression to solve for current yields $I = \frac{P}{V \cos(\phi)}$. Since $P$ and $V$ are considered constant for a given transmission scenario, the current $I$ is inversely proportional to the power factor $\cos(\phi)$.

Key Formulas: $P = VI \cos(\phi)$ — Relationship between power, voltage, current, and power factor; $I = \frac{P}{V \cos(\phi)}$ — Inverse proportionality between load current and power factor

Key Points: A lower power factor increases the current required to deliver the same amount of real power.; Higher current leads to increased $I^2R$ losses in the transmission line.; Transmission line capacity is often limited by the thermal limit imposed by current flow.

Advantages: High power factor leads to lower line currents; Lower currents result in reduced ohmic losses ($I^2R$)

Disadvantages: Low power factor necessitates larger conductor cross-sections to handle higher currents; Low power factor increases voltage regulation issues

Applications: Industrial power distribution; Grid management and power factor correction

Additional Info: Maintaining a high power factor (close to unity) is essential for efficient power system operation.. Options A, B, and D are incorrect because they fail to represent the physical relationship derived from the power equation.

Answer: C is correct — The load current is inversely proportional to the load power factor as derived from the real power equation $P = VI \cos(\phi)$.

Exam Tip: Always remember that for a fixed load, decreasing the power factor increases the line current, which directly impacts the copper losses and voltage drop of the transmission line.

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Option A: Load current is directly proportional to the load power factor.

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Option B: Load current is directly proportional to the square of load power factor.

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Option D: Load current is inversely proportional to the square of load power factor.

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