Inductance of transmission line is minimum when

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Examoogle · Accepted Answer

Option D: GMD is low and GMR is high

Explanation & Concepts:
The inductance of a transmission line is governed by its geometry, specifically defined by the Geometric Mean Distance (GMD) between conductors and the Geometric Mean Radius (GMR) of the conductors. Mathematically, inductance is directly proportional to the natural logarithm of the ratio of GMD to GMR.

Working Principle: The inductance per unit length is given by $L = 2 	imes 10^{-7} \ln\left(\frac{GMD}{GMR}ight) H/m$. To minimize this value, the numerator (GMD) must be as small as possible, and the denominator (GMR) must be as large as possible. GMR is effectively the 'self-GMD' of the conductor, representing its equivalent radius considering internal flux linkages, which increases with conductor diameter or bundling.

Key Formulas: $L = 2 	imes 10^{-7} \ln\left(\frac{GMD}{GMR}ight) H/m$ — Expression for inductance of a single-phase transmission line; $GMR = r' = r e^{-1/4}$ — Relation between GMR and actual conductor radius $r$

Key Points: Lowering GMD reduces the mutual flux linkage between conductors.; Increasing GMR effectively reduces internal flux linkages, lowering the inductance.; Bundle conductors are used in EHV lines specifically to increase GMR and reduce line inductance.; Transmission line series reactance is given by $X_L = 2\pi f L$.

Advantages: Lower inductance improves power transfer capability; Reduces the series reactive voltage drop

Disadvantages: Decreasing GMD significantly can increase corona loss; Increasing GMR (via bundling) increases the cost of materials

Applications: High Voltage Direct Current (HVDC) line design; Extra High Voltage (EHV) AC transmission line construction

Additional Info: GMD represents the distance between conductors.. GMR represents the self-inductance property of the conductor cross-section.. Option B is incomplete because it ignores the impact of GMD on the ratio.. Option A is incorrect because increasing GMD increases the total inductance.

Answer: D is correct — Since $L \propto \ln(\frac{GMD}{GMR})$, minimizing inductance requires decreasing GMD and increasing GMR.

Exam Tip: Always remember that bundling conductors is the standard engineering practice to increase GMR, which decreases inductive reactance and increases capacitance, thereby improving line performance.

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Option A: GMD is high

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Option B: GMR is high

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Option C: Both GMD and GMR are high

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