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A single-phase transmission line consists of two parallel conductors one meter apart and 1.25 cm in diameter. The loop inductance per km of the line is:


1. 21.3 × 10-4 Henry/ km
2.  34.3 × 10-7 Henry/ km
3. 11.5 × 10-7 Henry/ km
4. 19.5 × 10-7 Henry/ km

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Correct Answer - Option 1 : 21.3 × 10-4 Henry/ km

Concept:

The inductance of a transmission line consists of two parallel conductors is given by,

\(L=\frac{{{\mu }_{0}}}{\pi }\ln \left( \frac{d}{{{r}'}} \right)\) H/m

Where, d = distance between the conductors

r’ = 0.7788 r

r = radius of conductors

Calculation:

Given

d = 1 m

Diameter (D) = 1.25 cm

r = 0.625 cm = 0.625 × 10-2 m

r' = 0.7788 r

\(L=\frac{{{\mu }_{0}}}{\pi }\ln \left( \frac{d}{{{r}'}} \right)\) H/m

\(L=\frac{{{4\pi \times10^{-7} }_{}}}{\pi }\ln \left( \frac{d}{{{r}'}} \right)\)

\(L={{{4 \times10^{-7} }_{}}}{ }\ln \left( \frac{d}{{{r}'}} \right)\)

\(L={{{4 \times10^{-7} }_{}}}{ }\ln \left( \frac{1}{{{0.7788\times 0.625\times 10^{-2}}}} \right)\)

L = 21.3 × 10-4 Henry/ km

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