Question

The output of a generator is 440 V at 20 A. It is to be transmitted on a line with resistance of

0.60 ?. To what voltage must the generator output be stepped up with a transformer if the
power loss in transmission is not to exceed 0.010% of the original power?
A) 7.3 kV B) 45 kV C) 22 kV D) 30 kW E) 4.4 kV

Answer 1

Even though the question mentions some original power, the power to be transmitted remains the same as 8800 W

Therefore,

Power transmitted = 440 x 20 = V x I.

Where V and I are the current and voltage after stepping up or stepping down the voltage.

(Note that there is no original or unoriginal power, both remain the same, the voltage and current differ)

From the above equation there are unlimited values for V and I.

If any one of the voltage or current is given, we can find the other.

In the problem a way is given to find the value of this current.

It is given that power loss must be so much. That is .01 % of the original power.

This is a loss of power in the transmission line and is affected by the value of the current that the generator sends through it.

If 20 A passes through 0.6 ohm the loss will be = 0.6 x 20 x20 = 240 W.


Now starts the confusion.

What should be the power loss expected after the transformer is used? Should the loss be 0.01% of this original power loss of 240 W or 0.01 % of the generator power? What is in the mind of the questioner cannot be understood. I mean the person who set the question originally and not you who posted the question.

However, we can solve the problem taking one first and then the other.

If the loss is 0.01 % of 8800 W, then it is 0.88 W

Hence the current is limited to ? [0.88 /0 .6] = 1.21 A

Using this value of current in the original power balance equation

440 x 20 = V x I.

V = 7266.36 volt.


If the loss is 0.01 % of 240 W, then it is 0.024 W

Hence the current is limited to ? [0.024 /0 .6] = 0.2 A

Using this value of current in the original power balance equation

440 x 20 = V x I.

V = 44000 volt. = 44 kV

ans.E) 44 kV