University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 31 - Alternating Current - Problems - Exercises - Page 1044: 31.5

Answer

a. $\phi=90^{\circ}$. b. $f=193Hz$.

Work Step by Step

a. As seen in the caption to Figure 31.8b on page 1024, the phase angle is $\phi=90^{\circ}$. The source voltage leads the current by one-quarter cycle. b. $X_L=\frac{V}{I}=\frac{45.0V}{3.90A}=11.54\Omega$ Solve $X_L=2 \pi fL$ for the frequency. $$f=\frac{X_L}{2 \pi L}=\frac{11.54\Omega }{2 \pi (9.50\times10^{-3}H)}=193Hz$$
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