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 622: 48

Answer

$U_i=5.63\times10^{-5}J$, and 0.537 s.

Work Step by Step

Refer to section 21-11 to find the initial energy stored in the inductor. $$U_i=\frac{1}{2}LI^2=\frac{1}{2}(0.0450H)(0.0500A)^2=5.63\times10^{-5}J$$ If the energy increases by a factor of 5, since it is proportional to the square of the current, the final current is $\sqrt{5}$ times greater than the initial current. $$U_f=5U_i$$ $$I_f=\sqrt{5}I_i$$ The current increases at a constant rate, so find the time. $$\frac{\Delta I}{\Delta t}=0.115A/s = \frac{I_f-I_i}{\Delta t}$$ $$\Delta t =\frac{I_f-I_i}{0.115A/s }=\frac{\sqrt{5}I_i -I_i}{0.115A/s }$$ $$\Delta t =\frac{(\sqrt{5}-1)I_i }{0.115A/s }$$ $$\Delta t =\frac{(\sqrt{5}-1)0.050A }{0.115A/s }=0.537s$$
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