Test: Calculation of Capacitance of Transmission Line - Electrical Engineering (EE) MCQ

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

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

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 
Therefore the denominator as whole decreases and net capacitance increases.

Open-wire line:

The capacitance of an open-wire line is given by,

Where r is the radius of the conductor
d is the distance between the lines
Twin-lead wire:

The capacitance of a twin-lead wire is given by,

Where r is the radius of the conductor
D is the distance between the conductors
Coaxial cable:

The capacitance of a co-axial cable is given by,

Where b is the radius of the outer conductor
a is the radius of the inner conductor

Concept:
The capacitance of line:
The capacitance of each conductor to neutral is given by,

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

= 8.4 × 10^-12
The capacitance per km will be

Ds = 0.7788r = 0.7788 × 0.3 = 0.233 cm

= 1.38 × 10^-6 H/m
= 1.38 × 10^-3 H/km
The value of the inductance
L = 1.38 × 10^-3 × 125 = 0.1725 H

Inductance, L ∝ ln (D/r)
Capacitance 
Hence the inductance will increase and the capacitance will decrease