In a transmission line of negligible resistance , the surge impedance will be

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Option A: $\sqrt{\frac{L}{C}}$

Explanation & Concepts:
The surge impedance ($Z_s$) or characteristic impedance of a transmission line is defined as the square root of the ratio of its per-unit-length inductance ($L$) to its per-unit-length capacitance ($C$). For a lossless line where resistance is negligible, the surge impedance is purely resistive and is given by $Z_s = \sqrt{\frac{L}{C}}$.

Working Principle: The surge impedance arises from the transmission line's ability to store energy in its distributed magnetic and electric fields. As a voltage surge propagates, it experiences a ratio of voltage to current determined by the line's distributed parameters. In the absence of resistance, this ratio remains constant and purely resistive, representing the impedance a surge encounters as it travels along the line.

Key Formulas: $Z_s = \sqrt{\frac{L}{C}}$ — Surge impedance of a transmission line; $v = \frac{1}{\sqrt{LC}}$ — Velocity of propagation in a lossless line

Key Points: Surge impedance is independent of the line length.; It is measured in Ohms ($\Omega$).; For overhead lines, $Z_s$ typically ranges between 300 to 500 $\Omega$.; For underground cables, $Z_s$ is significantly lower, typically between 30 to 60 $\Omega$.

Advantages: Crucial for calculating the reflected and transmitted waves during transients.; Essential for designing protective equipment like lightning arresters.

Disadvantages: High surge impedance can lead to high voltage stresses at terminal points during switching operations.

Applications: Analysis of Traveling Waves in Power Systems.; Determination of natural loading (SIL) of transmission lines.

Additional Info: The Surge Impedance Loading (SIL) is defined as $P_{SIL} = \frac{V^2}{Z_s}$, representing the load at which the line absorbs as much reactive power as it generates.. Option B represents the reciprocal of surge impedance (admittance-like), while Option C is related to the propagation constant.

Answer: A is correct — The surge impedance of a transmission line with negligible resistance is defined as $\sqrt{\frac{L}{C}}$.

Exam Tip: Always remember that $Z_s$ depends on the physical geometry of the conductors, whereas $Z_0$ (characteristic impedance) in cables is lower due to higher capacitance between conductors and the sheath.

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Option B: $\sqrt{\frac{C}{L}}$

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Option C: $\frac{1}{\sqrt{LC}}$

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Option D: $\sqrt{LC}$

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