Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 18 - Electric Currents - General Problems - Page 524: 75

Answer

See answer.

Work Step by Step

a. We know that P = IV, so if power P is delivered using voltage V, the current I=P/V. This current passes through the transmission line of resistance R. The power lost in the wire is $I^2R$ due to heating of the wire. This transmission loss is $I^2R=(\frac{P}{V})^2R=\frac{P^2R}{V^2}$ which was to be shown. b. The transmission loss is inversely proportional to the square of V, so V should be as large as possible.
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