Question

The figure shows the arrangement of conductors a and a' in parallel form in one circuit, while conductors b and b' in parallel form in the return path. Conductor diameter is 2 cm. The total inductance of the line per km (assuming that the current is equally shared by the two parallel conductors) is ______$mH/km$.

• A. 1.305

Answer 1

The correct option is A 1.305
Loop inductance/km

$L=4\times {10}^{-4}ln\frac{D_m}{D_s}H/km$

Mutual inductance
$D_m={(D_{ab}\times D_{ab}\times D_{a{b}^{\prime }}\times D_{a^{\prime }{b}^{\prime }})}^{1/4}$

$={(90\times 75\times 105\times 90)}^{1/4}=89.36cm$

Self inductance
$D_s={(D_{aa}\times D_{a{a}^{\prime }}\times D_{a^{\prime }a}\times D_{a^{\prime }a})}^{1/4}$

$D_{aa}=D_{a^{\prime }a}=0.7788r=0.7788\times 1=0.7788cm$

$D_s={(0.7788\times 15\times 15\times 0.7788)}^{1/4}=3.417cm$

$L=4\times {10}^{-4}\times ln\left(\frac{89.36}{3.417}\right)H/km$
$L=1.305mH/km.$