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?

Open-wire line:

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

\(C = \frac{{\pi \varepsilon }}{{\ln \left( {\frac{d}{r}} \right)}}\)

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,

\(C = \frac{{\pi \varepsilon }}{{\ln \left( {\frac{D}{r}} \right)}}\)

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,

\(C = \frac{{2\pi \varepsilon }}{{\ln \left( {\frac{b}{a}} \right)}}\)

Where b is the radius of the outer conductor

a is the radius of the inner conductor

Application:

• For a given radius r of the conductor, the distance between the conductors in the twin-lead wire is less than the open wire line and hence the capacitance is lesser in the open wireline.
• In a coaxial cable, the ratio of b/a is very small and hence capacitance is large.
• The capacitance per unit length of the open-wire line is least.