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A power of 100 kW (105 W) is delivered to the other side

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QUESTION:

A power of 100 kW (\(10^{5}\) W) is delivered to the other side of a city by a pair of power lines, between which the voltage is 12,000 V. (a) Use the formula P = IV to show that the current in the lines is 8.3 A. (b) If each of the two lines has a resistance of 10 \(\Omega\), show that there is a 83-V change of voltage along each line. (Think carefully. This voltage change is along each line, not between the lines.) (c) Show that the power expended as heat in both lines together is 1.38 kW (distinct from power delivered to customers). (d) How do your calculations support the importance of stepping voltages up with transformers for long-distance transmission?

Text Transcription:

10^5

Omega

Questions & Answers

QUESTION:

A power of 100 kW (\(10^{5}\) W) is delivered to the other side of a city by a pair of power lines, between which the voltage is 12,000 V. (a) Use the formula P = IV to show that the current in the lines is 8.3 A. (b) If each of the two lines has a resistance of 10 \(\Omega\), show that there is a 83-V change of voltage along each line. (Think carefully. This voltage change is along each line, not between the lines.) (c) Show that the power expended as heat in both lines together is 1.38 kW (distinct from power delivered to customers). (d) How do your calculations support the importance of stepping voltages up with transformers for long-distance transmission?

Text Transcription:

10^5

Omega

ANSWER:

Step 1 of 6

In order to answer this question, we need to write down the relation between power with current and voltage which is given by

 …. Equation 1

Also, we will need to use the Ohm's law which states that

 …. Equation 2

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