For a given conductor the value of GMR is

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Option A: Larger for capacitance calculation

Explanation & Concepts:
In transmission line analysis, the Geometric Mean Radius (GMR) is used for inductance calculations to account for internal flux linkage, whereas capacitance calculations use the actual physical radius (r) of the conductor because surface charge distribution results in zero internal electric field.

Working Principle: For inductance, $L = 2 	imes 10^{-7} \ln(\frac{D}{GMR})$ where $GMR = r' = r e^{-1/4} \approx 0.7788r$. For capacitance, $C = \frac{2\pi \epsilon}{\ln(D/r)}$, effectively using the physical radius $r$. Since $r > 0.7788r$, the 'effective radius' used in the capacitance formula is larger than the GMR used in the inductance formula.

Key Formulas: $L = 2 	imes 10^{-7} \ln(\frac{D}{GMR})$ — Inductance calculation using GMR ($r' = 0.7788r$); $C = \frac{2\pi \epsilon}{\ln(D/r)}$ — Capacitance calculation using physical radius $r$

Key Points: GMR accounts for internal flux linkage within the conductor.; Capacitance depends only on the charge on the surface, hence internal flux is irrelevant.; The physical radius $r$ is always greater than the GMR ($0.7788r$).; GMR is a geometric property based on the arrangement and shape of strands.

Advantages: Simplifies complex inductance calculations for stranded conductors.; Provides a unified method to handle internal and external flux.

Disadvantages: GMR is not physically measurable like the radius.; Requires specific tables or calculations for different conductor geometries.

Applications: Overhead transmission line design.; Power system steady-state analysis.

Additional Info: For solid round conductors, $GMR = r e^{-1/4}$.. Option B is incorrect because GMR is smaller than $r$, not larger.. Option C is incorrect because the internal flux linkage behavior differs between electrostatic and magnetic fields.

Answer: A is correct — The GMR is used for inductance calculations, making the equivalent radius used in capacitance calculations (which is just $r$) larger.

Exam Tip: Always remember: Inductance involves internal magnetic flux (GMR), while capacitance involves surface electric charge (Physical radius $r$).

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Option B: Larger for inductance calculation

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Option C: Same for capacitance and inductance calculation

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Option D: None of above

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