Question

A 3-phase, 50 Hz transmission line of length 100 km has a capacitance of $\frac{0.03}{\pi }\mu F/Km.$
It is represented as a $\pi$-model. The shunt admittance at each end of the transmission line will be

• A. $600\times {10}^{-6}\angle {90}^o\mho$
• B. $150\times {10}^{-6}\angle {90}^o\mho$
• C. $\frac{{10}^{-6}}{150}\angle {90}^o\mho$
• D. $300\times {10}^{-6}\angle {90}^o\mho$

Answer 1

The correct option is B $150\times {10}^{-6}\angle {90}^o\mho$

In $\pi$ model, the shunt admittance at each end of the line is $\frac{Y}{2}$.

$\frac{Y}{2}=j\omega \frac{C}{2}=j(2\pi \times 50)\times \frac{0.03}{\pi }\times \frac{1}{2}\times {10}^{-6}\times 100$

$=150\times {10}^{-6}\angle {90}^o\mho$