Question

Consider the following types of transmission lines:
1.Open-wire line
2. Twin-lead wire
3.Coaxial cable
The capacitance per metre will be least in which of the above transmission lines?

• A. 1 only
• B. 2 only
• C. 1, 2 and 3
• D. 3 only

Answer 1

The correct option is C 1, 2 and 3

Open-wire line :
The capacitance of an open-wire line is given by,
$C=\frac{\pi \epsilon }{\ln \left(\frac{d}{r}\right)}$
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,
$C=\frac{\pi \epsilon }{\ln \left(\frac{D}{r}\right)}$
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,
$C=\frac{2\pi \epsilon }{\ln \left(\frac{b}{a}\right)}$
Where b is the radius of the outer conductor a is the radius of the inner conductor
For the conductors of same radius, distance between the conductors of twin-lead wire is less than that of open-wire line, Hence, capacitance of open-wire line is less than that of twin-wire line.
In coaxial cable, the ratio b/a is less. Hence, capacitance of coaxial cable is more.
Hence, open-wire line has least capacitance.