If the line is loaded with the surge impedance, the receiving end voltage

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Option B: Equal to sending end voltage

Explanation & Concepts:
When a transmission line is loaded with a resistive load equal to its surge impedance ($Z_C$), the receiving end voltage is equal to the sending end voltage. This state is known as Surge Impedance Loading (SIL).

Working Principle: The surge impedance is defined as $Z_C = \sqrt{\frac{L}{C}}$. When a line is terminated with $Z_C$, the traveling wave is completely absorbed by the load without reflection. Since there is no reflected wave, the voltage and current profiles remain constant along the length of the line, resulting in $V_R = V_S$.

Key Formulas: $Z_C = \sqrt{\frac{L}{C}}$ — Surge impedance of a transmission line; $P_{SIL} = \frac{V^2}{Z_C}$ — Power delivered at surge impedance loading

Key Points: At SIL, the reactive power generated by line capacitance is exactly absorbed by line inductance.; The voltage profile along the line is flat when loaded with surge impedance.; SIL represents the capacity of the line to transmit power without requiring external compensation.

Advantages: Flat voltage profile along the line; No reactive power compensation needed

Disadvantages: Limited power transfer capacity; Does not account for line resistance

Applications: Designing EHV transmission systems; Assessment of transmission line efficiency

Additional Info: The surge impedance for overhead transmission lines typically ranges between $350 \Omega$ to $450 \Omega$.. If the load impedance is greater than $Z_C$, the receiving end voltage rises (Ferranti effect at no load).

Answer: B is correct — When a transmission line is loaded with its surge impedance, the traveling waves do not reflect, maintaining a constant voltage profile where the receiving end voltage equals the sending end voltage.

Exam Tip: Always remember that for load impedance $Z_L > Z_C$, $V_R > V_S$, and for $Z_L

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Option A: Less than sending end voltage

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Option C: More than sending end voltage

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Option D: None of above

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