If a balanced three phase three wire line consistance of thr

If a balanced three phase three wire line consistance of three cylindrical conductors of the same radius r and equally spaced D apart has an inductance per phase of 2 * 10^-7 Ln(D/r\') H/m, why does a single phase two wire line consisting of two cylindrical conductors of the same radius and spaced D apart have an inductance of 4 * 10^-7 Ln(D/r\') H/m?

Solution

Inductance of Single Phase Two Wire Line

A single phase line consists of two parallel conductors which form a rectangular loop of one turn. When an alternating current flows through such a loop, a changing magnetic flux is set up. The changing flux links the loop and hence the loop possesses inductance. It may appear that inductance of a single phase line is negligible because it consists of a loop of one turn and the flux path is through air of high reluctance. But as the cross -sectional area of the loop is very large, even for a small flux density, the total flux linking the loop is quite large and hence the line has appreciable inductance.