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  • 1MW power is to be delivered from a power station to a town 10 km away. One uses a pair of Cu wires of radius 0.5 cm for this purpose. Calculate the fraction of ohmic losses to power transmitted if

1MW power is to be delivered from a power station to a town 10 km away. One uses a pair of Cu wires of radius 0.5 cm for this purpose. Calculate the fraction of ohmic losses to power transmitted if

(i) power is transmitted at 220V. Comment on the feasibility of doing this.
(ii) a step-up transformer is used to boost the voltage to 11000 V, power transmitted, then a step-down transformer is used to bring voltage to 220 V.
(\rho _{cu}=1.7\times10^{-8} SI \; unit)

 

Answers (1)

L=20\; km=20000\; m

R=\rho _{cu}\frac{L}{A}=\frac{1.7*10^{-8}*2*10^{4}}{\pi (0.5*10^{-2})^{2}}=4\Omega

I=\frac{10^{6}}{220}=0.45*10^{4}A

Power loss = I^{2}R=4*0.45^{2}*10^{8}>10^{6}W

ii) P=10^{6}

V'=11000 \; V

I'=\frac{P}{V'}=\frac{1}{1.1}*10^{2}

Power Loss =

I'^{2}R=\frac{1}{1.21}*4*10^{4}=3.3*10^{4}W

Fraction of power loss =

\frac{3.3*10^{4}}{10^{6}}=3.3\; ^{o}/_{o}

Posted by

infoexpert23

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