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: 51

Answer

3.7 time constants.

Work Step by Step

The current through the LR circuit after the battery is removed is given by the following equation, discussed in section 21-12. $$I=I_{max}e^{-t/\tau}$$ $$\frac{I}{ I_{max}}= e^{-t/\tau} $$ Set I equal to 2.5 percent of its original value, and solve for the time t. $$0.025= e^{-t/\tau}$$ $$t=-\tau ln(0.025)\approx 3.7\tau $$ It takes 3.7 time constants.
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