A hydroelectric power plant situated at a distance of 20 km from a town. Whose energy demand is 100 MW at 240 V. At hydro electric power plant, the water pressure head is at a height of 400 m and the water flow available is 100 m³/s. Electrical energy generated in power plant is transmitted to the town with the use of transformers voltage output of the Ac. generator at power plant is stepped up and is there transmitted over long distances to an sub-station near the consumers in town. Sub-stations and utility poles steps down the voltage finally the 240 V which finally reaches the houses.

Resistance of the two wires transmitting the power is 1 Ω/km. If the 50,000 – 5000 V step down transformer is used at a sub-station in town, the power loss in transmission line in the form of heat is

160 MW

The correct answer is Option (4) →160 MW

Here net resistance of power line

$R =1 \frac{\Omega}{km} \times 40 ~km$

$=40 \Omega$

Current in line $I=\frac{P}{V}=\frac{100 \times 10^6}{50,000}$

$I=2 \times 10^3 ~A$

∴  Power loss in line $P_{\text {loss }}=I^2 R$

$P_{\text {loss }}=\left(2 \times 10^3\right)^2(40)$

$=160 \times 10^6 ~W$

$P_{\text {loss }}=160 ~MW$