Question

Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length $D_{ab}=D_{bc}=D_{ca}=1m$ as shown in figure below. The resistances of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01m. Neglecting the effect of ground, the magnitude of positive sequence reactance in $\Omega /km$ (rounded off to three decimal places) is ____

• A. 0.2893

Answer 1

The correct option is A 0.2893
$L=2\times {10}^{-7}\ln \left(\frac{GMD}{GMR}\right)H/m$

$D_{ab}=D_{bc}=D_{ca}=1m$

$GMD=1m$

$GMR=0.01m$

frequency, f = 50 Hz

$L=2\times {10}^{-7}\ln \left(\frac{1}{0.01}\right)H/m$

$=9.21\times {10}^{-7}H/m$

$X_L=2\pi fL$

$=2\pi \times 50\times 9.21\times {10}^{-7}$

$=0.2893\times {10}^{-3}\Omega /m$

$=0.2893\Omega /km$