The presence of earth in case of overhead transmission line

The correct answer is 'option 1' (increases capacitance).

Concept: 

The capacitance of overhead transmission lines when the earth effect is neglected is given by

\(C={2\pi\epsilon\over log{D\over r}}\)

The capacitance of overhead transmission lines when the earth effect is considered is given by

\(C={\pi\epsilon\over log{D\over r\sqrt{1+{d^2\over 4h^2}}}}\)

In the above expressions, D is the interspacing distance between conductors, r is the radius of the conductors, and h is the height of the transmission line from the ground.

It can be observed that the presence of earth modifies the radius of the conductor from r to \(r\sqrt{1+{d^2\over4h^2}}\). Therefore the denominator as whole decreases and net capacitance increases.

 Important PointsAs the earth is considered to be a pool of infinite electrons, the presence of an overhead transmission line causes charge carriers to separate by a dielectric(air), thereby increasing the capacitance.