# GATE Papers >> EEE >> 2019 >> Question No 59

Question No. 59

A three-phase 50 Hz, 400 kV transmission line is 300 km long. The line inductance is 1 mH/km per phase, and the capacitance is 0.01 µF/km per phase. The line is under open circuit condition at the receiving end and energized with 400 kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be ___________.

##### Answer : 414.00 to 423.00

Solution of Question No 59 of GATE 2019 EEE Paper

Given, line length = 300 km long (means long line).

$\begin{array}{l}{\mathrm V}_{\mathrm S}=400\mathrm{kV}\left(\mathrm{line}\;\mathrm{to}\;\mathrm{line}\right).\mathrm L=1\mathrm m\;\mathrm H/\mathrm{km}\;\mathrm{and}\;\mathrm C=0.01\mathrm{μF}/\mathrm{km}.\\\mathrm V(\mathrm{speed})=\frac1{\sqrt{\mathrm{LC}}}=\frac1{\sqrt{0.01\times10^{-6}\times1\times10^3}}=316227.766\mathrm{km}/\mathrm s.\\\mathrm A=1-\frac{\mathrm\beta^2}2=1-\frac{\left({\displaystyle\frac{2\mathrm{πf}\mathcal l}{\mathrm V}}\right)^2}2=1-\frac{\left({\displaystyle\frac{2\mathrm\pi\times50\times300}{316227.766}}\right)^2}2=0.955.\\{\mathrm V}_{\mathrm r(\mathrm{Noload})}=\frac{{\mathrm V}_{\mathrm s}}{\mathrm A}=\frac{400}{0.955}=418.59\mathrm{kV}.\end{array}$

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