A single phase transmission line has two parallel conductors 3 m apart, the radius of each conductor being 1 cm. Calculate the loop inductance per km length of the line if the material of the conductor is (i) copper (ii) steel with relative permeability of 100

Spacing of conductors, d = 300 cm
Radius of conductor, r = 1 cm
Loop inductance = 10
−7 (μr
+ 4 loge
d/r) H/m
(i) With copper conductors, μr
= 1
∴ Loop inductance/m = 10
−7 (1 + 4 loge
d/r) H
= 10
−7 (1 + 4 loge
300/1) H = 23·8 × 10
−7 H
Loop inductance/km = 23·8 × 10
−7 × 1000 = 2·38 × 10
−3 H = 2·38 mH
(ii) With steel conductors, μ r
= 100
∴ Loop inductance/m = 10
−7 (100 + 4 loge
300/1) H = 122·8 × 10
−7 H
Loop inductance/km = 122·8 × 10
−7 × 1000 = 12·28 × 10
−3 H = 12·28 mH

12