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