Reasoning:

The inductance of a transmission line depends on various parameters like the length of the line, the distance between the conductors, the radius of the conductors, and the permeability of the surrounding medium. The formula for calculating the inductance of a transmission line is given by:

L = μ/2π × ln(D/d)

where L is the inductance per unit length, μ is the permeability of the surrounding medium, D is the distance between the conductors, and d is the radius of the conductors.

When the conductor radius increases, the distance between the conductors also increases, and hence, the inductance of the line decreases.

Explanation:

The following points explain why the inductance of the line decreases when the conductor radius increases:

- Effect of conductor radius on distance between the conductors: The distance between the conductors is directly proportional to the conductor radius. When the radius of the conductor increases, the distance between the conductors also increases. This is because the conductors are usually placed at a fixed distance from each other, and when the radius of the conductor increases, the space between the conductors decreases. This decrease in space between the conductors leads to an increase in the distance between them.

- Effect of distance between the conductors on inductance: The inductance of a transmission line is inversely proportional to the distance between the conductors. This means that as the distance between the conductors increases, the inductance of the line decreases. The reason for this is that the magnetic field generated by the current flowing through one conductor is weaker at a greater distance from the conductor. Hence, a greater distance between the conductors means that the magnetic field generated by one conductor is weaker at the position of the other conductor, resulting in a lower inductance.

- Effect of inductance on transmission line performance: The inductance of a transmission line affects its performance in various ways. An increase in inductance leads to a higher voltage drop across the line for a given current, which can reduce the efficiency of the line. It can also lead to a higher reactive power consumption, which can affect the power factor of the line. Hence, it is desirable to have a lower inductance for a transmission line.

Conclusion:

In summary, the inductance of a transmission line decreases when the conductor radius increases. This is because the increase in conductor radius leads to an increase in distance between the conductors, which in turn leads to a decrease in inductance. A lower inductance is desirable for a transmission line as it leads to better performance and efficiency.