Question

A power plant produces 1000 MW to supply a city 40 km away. Current flows from the power plant on a single wire of resistance 0.050 Ω/km, through the city, and returns via the ground, assumed to have negligible resistance. At the power plant the voltage between the wire and ground is 115 kV.
(a) What is the current in the wire?
(b) What fraction of the power is lost in transmission?

Answer 1

Our values are given as,

$P_{plant} = 1000MW$

$V = 115kV = 115*10^3V$

$L = 40Km$

PART A)

Power is defined as the product between the current and the voltage, therefore the current would be

$I = \frac{P}{V}$

$I = \frac{1000}{115*10^3}$

$I = 8704.34A$

PART B) The resistance unit length is,

$\frac{R}{L} = 0.05\Omega /km$

$R = 0.05*40$

$R = 2\Omega$

Therefore for the calculation of the loss of Power we would have to apply the relation:

$P_{l} = I^2 R$

$P_l = (8704.34)^2*2$

$P_l = 151.53MW$

Fraction loss power transmission is,

$\frac{P_l}{P_{plant}} = \frac{151.53}{1000}$

$\frac{P_l}{P_{plant}} = 0.151$

$\frac{P_l}{P_{plant}} = 15.1\%$