Physics: Principles with Applications (7th Edition)

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

Chapter 21 - Electromagnetic Induction and Faraday's Law - Problems - Page 621: 35

Answer

6 billion meters.

Work Step by Step

Find the initial current from equation 18–9a. $$P=IV$$ $$I=\frac{P}{V}=\frac{100\times10^3 W}{12\times10^3 V}=8.333A$$ Next in line is the step-up transformer, multiplying the voltage by a factor of 20, therefore lowering the secondary current by the same factor. $$I_S=8.333A/20 = 0.41667 A$$ Calculate the power lost, which is the dissipated power. We set the power lost to 50 kW. $$P_{loss}=I^2 R=50\times10^3W=(0.41667 A)^2 (5\times10^{-5}\Omega/m)L$$ Find the length of wire L that loses that much power. $$L=\frac{50\times10^3W}{(0.41667 A)^2 (5\times10^{-5}\Omega/m)}$$ $$L\approx 6\times10^9 m$$
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