Question

In: Physics

A generator at a utility company produces 100 A of current at 4.0 x 103 V....

A generator at a utility company produces 100 A of current at 4.0 x 103 V. The voltage is stepped up to 2.4 x 105 V by a transformer before being sent on a high voltage line across a rural area to a city. Assume the effective resistance of the line is 30.0 Ω and the transformers are ideal.

a. Determine the percentage of power lost in the transmission line.

b. What percentage would be lost if the voltage would not have been stepped up?

c. How many kW-hr of energy is lost each day if the voltage would not have been stepped up?

d. Calculate the cost of this energy loss if the price of electricity is $.11/kW-hr.

Solutions

Expert Solution

The generator produces of current at .

The power produced by the generator is

Since the input and output power to a transformer remains the same, we can calculate the output current of the transformer

Part A

The power lost due to resistance can be calculated by the formula

The current we consider is the output current of the transformer, .

The percentage of power lost will be equal to

Part B

If the power is not stepped up, it would have the original amperage of .

The percentage of power loss would be

This is much higher than the original power loss, and is the reason why voltages are stepped up, to prevent resistive(Ohmic) losses.

Part C

The powerloss is

The energy lost in an hour is

The energy lost in a day will be twenty-four times this.

Part D

The cost of this energy loss will be the daily energy loss times the cost per kilo-watt hour.

genius_generous answered 5 months ago

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