Question

A 500 km long transmission line has series impedance of $(0+j0.5)\Omega /km$ and the shunt admittance of (0 + j5) $\mu$mho/km. The magnitude of the characteristic impedance in ohm of the equivalent $\pi$-circuit of the transmission line will be

• A. 141.72 $\Omega$
• B. 316.22 $\Omega$
• C. 158.11 $\Omega$
• D. 283.44 $\Omega$

Answer 1

The correct option is B 316.22 $\Omega$

Given, series impedance: (0 + j0.5) $\Omega$/km

For 500 km : Z=j250 $\Omega$

Similarly,
shunt admittance = (0 + j5) $\mu$mho/km

for 500 km : Y=(0 + j5)×${10}^{-6}\times 500=(0+j2.5\times {10}^{-3})$$\mho$

Characteristic impedance,

$Z_C=\sqrt{\frac{Z}{Y}}$

$Z_C=\sqrt{\frac{250}{250\times {10}^{-3}}}=316.22\Omega$