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A thermal power plant produces electric ...

A thermal power plant produces electric power of `600 kW` at `4000 V`, which is to be transported to a place `20 km` away from the power plant for consumers' usage.It can be transported either directly with a cable of large current capacity or by using a combination of step-up and step-down transformers at the two ends.The drawback of the direct transmission is the large energy dissipation.In the method using transformer, the dissipation is much smaller.In this method, a step-up transformer 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 resistive and the transformers are ideal with a power factor unity.All the currents and voltages mentioned are `rms` values.
If the direct transmission method with a cable of resistance `0.4 Omega km^(-1)` is used, the power dissipation (in `%`) during transmission is

A

`200:1`

B

`150:1`

C

`100:1`

D

`50:1`

Text Solution

Verified by Experts

The correct Answer is:
A

`N_(P)/N_(S)=40,000/200=200/1`
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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. In the method using the transformers assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1:10 if the power to the consumers has to be supplied at 200V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is

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