Physics Class 12 NCERT Solutions: Chapter 7 Alternating Current Part 10

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Symbol of Transformer

Symbol of Transformer

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Q: 25. A small town with a demand of of electric power at is situated away from an electric plant generating power at. The resistance of the two wire line carrying power is. The town gets power from the line through a step-down transformer at a sub-station in the town.

(A) Estimate the line power loss in the form of heat.

(B) How much power must the plant supply, assuming there is negligible power loss due to leakage?

(C) Characterise the step up transformer at the plant.

Answer: Total electric power required,

Supply voltage,

Voltage at which electric plant is generating power,

Distance between the town and power generating station,

Resistance of the two wire lines carrying power

Total resistance of the wires,

A step-down transformer of rating is used in the sub-station.

Input voltage,

Output voltage,

Rms current in the wire lines is given as:

(A) Line power loss

(B) Assuming that the power loss is negligible due to the leakage of the current:

Total power supplied by the plant

(C) Voltage drop in the power line

Hence, total voltage transmitted from the plant

Also, the power generated is 440 V.

Hence, the rating of the step-up transformer situated at the power plant is 440 V – 7000 V.

Q: 26. Do the same exercise as above with the replacement of the earlier transformer by a step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred?

Answer:

The rating of a step-down transformer is.

Input voltage,

Output voltage,

Total electric power required,

Source potential,

Voltage at which the electric plant generates power,

Distance between the town and power generating station,

Resistance of the two wire lines carrying power

Total resistance of the wire lines,

Rms current in the wire line is given as:

(A) Line power loss

(B) Assuming that the power loss is negligible due to the leakage of current.

Hence, power supplied by the plant

(c) Voltage drop in the power line

Hence, voltage that is transmitted by the power plant

The power is being generated in the plant at.

Hence, the rating of the step-up transformer needed at the plant is

.

Hence, power loss during transmission

In the previous exercise, the power loss due to the same reason is. Since the power loss is less for a high voltage transmission, high voltage transmissions are preferred for this purpose.