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 - Problems - Page 523: 52

Answer

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Work Step by Step

a. Use Equation 18–9c to find the rms voltage. $$\overline{P}=\frac{V_{rms}^2}{R}$$ $$V_{rms}=\sqrt{\overline{P}R}=\sqrt{(100W)(8\Omega)}=28.3V\approx 30V$$ Now apply equation 18–9a to find the rms current. $$I_{rms}=\frac{\overline{P}}{V_{rms}}=\frac{100W}{28.28V}\approx 4A$$ b. Do the same thing, using the small power. $$\overline{P}=\frac{V_{rms}^2}{R}$$ $$V_{rms}=\sqrt{\overline{P}R}=\sqrt{(1.0W)(8\Omega)}=2.83V\approx 3V$$ Now apply equation 18–9a to find the rms current. $$I_{rms}=\frac{\overline{P}}{V_{rms}}=\frac{1.0W}{2.828V}\approx 0.4A$$
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