Question

A power plant produces 1000 MW to suply a city 40Km away.Current flows from the power plant on a single wire of resistance0.050 Ω/Km, through the city, and returns via the ground,assumed to have negligible resistance. At the power plant thevoltage between the wire and the ground is 115kV. a) What is thecurrent in the wire?. b) What fraction of the power is lostin transmission?

Answer 1

Answer:

The current in wire resistance 2Ω

a). 8696 A

b). fraction power 15.1% a 115kV

Explanation:

Resistance

$R=0.05$Ω/Km*40km

R=2Ω

P=1000 MW

a).

$P=V*I\\I=\frac{P}{V}=\frac{1000x10^{6}W}{115x10^{3}k } =8696.65A$

Using law ohm

b).

$V=I*R\\I=\frac{V}{R}$

$P=I*I*R\\P=I^{2} *R\\P=8696.65^{2}*2\\P=151.228 x10^{6} W$

$e=\frac{151.228x10^{6} }{1000x10^{6} }*100= 15.12$%