The inductance of power transmission line increases with

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Option C: Increase in spacing between the conductors

Explanation & Concepts:
The inductance of a transmission line is directly proportional to the flux linkages per ampere of current. As the spacing between conductors increases, the flux linkage per unit current increases, resulting in higher line inductance.

Working Principle: The inductance of a two-wire transmission line is given by the expression $L = 4 	imes 10^{-7} \ln(\frac{D}{r'}) H/m$. The term $D$ represents the Geometric Mean Distance (GMD) or the spacing between the conductors, while $r'$ is the Geometric Mean Radius (GMR). Since the natural logarithm function $\ln(D)$ is an increasing function of $D$, increasing the spacing between conductors leads to a logarithmic increase in the line inductance.

Key Formulas: $L = 2 	imes 10^{-7} \ln(\frac{D}{r'}) 	ext{ H/m}$ — Inductance for a single-phase transmission line; $GMD = \sqrt[3]{D_{ab}D_{bc}D_{ca}}$ — Geometric Mean Distance for 3-phase configuration

Key Points: Inductance increases logarithmically with the spacing between conductors.; Inductance decreases with an increase in the conductor radius (r').; GMR (Geometric Mean Radius) accounts for internal flux linkages of the conductor.; Inductance is independent of the load current carried by the line.

Advantages: Increased spacing reduces the risk of corona discharge by lowering the electric field intensity.; Spacing design allows for better insulation coordination.

Disadvantages: High inductance leads to higher voltage drops in the line.; Increased spacing requires larger, more expensive transmission towers.

Applications: Design of overhead transmission lines.; Calculation of line impedance for power system stability analysis.

Additional Info: Increasing the conductor diameter (Option B) effectively increases the GMR ($r'$), which decreases the inductance.. Line length affects total impedance ($Z=j\omega L 	imes l$), but not the inductance per unit length.. Load current does not affect the self-inductance of the line, which is a physical geometric property.

Answer: C is correct — The inductance of a transmission line increases as the distance between the conductors increases due to increased flux linkage.

Exam Tip: Always remember that inductance depends on physical geometry (spacing, radius, bundling), whereas resistance depends on material properties and temperature.

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Option A: Decrease in line length

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Option B: Increase in diameter of conductor

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Option D: Increase in load current carried by conductor

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