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The horizontally placed conductors of a single phase line operating at 50 Hz are having outside diameter of 1.6 cm, and the spacing between centers of the conductors is 6 m. The permittivity of free space is 8.854 × 10-12 F/m. The capacitance to ground per kilometer of each line is
1. 4.2 × 10-9 F
2. 8.4 × 10-9 F
3. 4.2 × 10-12 F
4. 8.4 × 10-12 F

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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

\(= \frac{C}{{km}} = 8.4 \times {10^{ - 9}}F\)

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