A thermal power plant produed electric power of 600kW at 4000V, which is to be transported to a place 20 km away form the power plant for consumer's usage. It can be transported either directly with a cable of large current carrying capacity or by sing a combination of step-up and step-down transfprmers at the two ends. THe drawback of the direct transmission is the large energy dissipation. In the method wsing transformers, the dissipatiion is much smaller. In this method a step-up transformers is used at the plant side so that the current is reduced to a smaller value. At the consumers'end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resostive and the transformers are ideal with power factor unity. All the currents and voltagementioned are values.
If hte direct transmission method with a cable of resistance `0.4(omega) km^(-1)` is used, the power dissipation (in %) during transmission is

Options

A. `20`
B. `30`
C. `40`
D. `50`

Answer

B

Explanation

Total resistance `=0.4xx20=8 Omega`
`P=Vi`
`Ϸ 600xx103=4000xxi`
`Ϸ i=600/4=150 A`
`P=i^(2)R`
`=(150)^(2)xx8`
`=22500xx8`
`=180000 watt`
`=180 kW`
`% loss=180/600' 100=30%`