Correct Answer - Option 2 : 8.4 × 10
-9 F
Concept:
The capacitance of line:
The capacitance of each conductor to neutral is given by,
\(C_{an}=\frac{2\pi\epsilon_{0}}{ln(\frac{d}{r})}\)
Where,
d = distance between the conductors
r = radius of conductors
Calculation:
Diameter of conductor = 1.6 m
Radius, r = 0.8 m
Distance d = 6m
The capacitance of each line os
\(C = \frac{{2\pi {\varepsilon _o}}}{{\ln \left( {\frac{d}{r}} \right)}} = \frac{{2\pi \times 8.85 \times {{10}^{ - 12}}}}{{\ln \left[ {\frac{6}{{0.8 \times {{10}^{ - 2}}}}} \right]}}\)
= 8.4 × 10-12
The capacitance per km will be
\(= \frac{C}{{km}} = 8.4 \times {10^{ - 9}}F\)