Surge impedance of transmission line is

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Option A: Independent of length

Explanation & Concepts:
The surge impedance ($Z_s$) 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 ($C$). Since both $L$ and $C$ are inherent distributed properties of the line geometry and material, $Z_s$ depends solely on the line construction and is entirely independent of the line's length.

Working Principle: For a lossless transmission line, the surge impedance is given by $Z_s = \sqrt{\frac{L}{C}}$. Because $L$ (Henry/meter) and $C$ (Farad/meter) are constants derived from the physical configuration of the conductors, any increase in length adds proportional amounts of both inductance and capacitance, causing the ratio $\frac{L}{C}$ to remain constant. Thus, the characteristic impedance (or surge impedance) remains fixed regardless of the line length.

Key Formulas: $Z_s = \sqrt{\frac{L}{C}}$ — Definition of surge impedance for a lossless line.; $Z_s = \sqrt{\frac{R + j\omega L}{G + j\omega C}}$ — General expression for a lossy transmission line.

Key Points: Surge impedance is also known as characteristic impedance ($Z_0$).; Typical values for overhead lines range from $400\Omega$ to $600\Omega$.; Typical values for underground cables range from $30\Omega$ to $50\Omega$.; It is a purely resistive value at high frequencies where losses are negligible.

Advantages: Used to determine the surge impedance loading (SIL) of a line.; Critical for calculating transient voltage reflections at line terminals.

Disadvantages: Not easily measurable using standard low-frequency meters.; Variation occurs if temperature significantly alters dielectric properties or conductor sag (though negligible in standard calculations).

Applications: Power system protection analysis.; High-voltage transmission line design.; Transient stability studies.

Additional Info: Option B is incorrect because $L$ and $C$ scale linearly with length $l$; since they are in a ratio, the length cancels out mathematically ($Z_s = \sqrt{\frac{Ll}{Cl}} = \sqrt{\frac{L}{C}}$).. Option C/D: Surge impedance is essentially independent of temperature as the primary constants ($L$ and $C$) are determined by geometric dimensions (spacing and radius).

Answer: A is correct — Surge impedance is an intrinsic property of the transmission line's physical configuration (inductance and capacitance per unit length) and does not scale with the total length of the line.

Exam Tip: Always remember that characteristic impedance is a property of the transmission medium, not the length of the link. It is analogous to the 'impedance' of space in electromagnetic waves.

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Option B: Dependent on length

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Option C: Dependent on temperature

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Option D: Independent of temperature

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