University Physics with Modern Physics (14th Edition)

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

Chapter 30 - Inductance - Problems - Exercises - Page 1019: 30.74

Answer

Choice A.

Work Step by Step

As seen in the previous problem, the current in the circuit is $i=i_0e^{-Rt/L}$. Solve for the time $t_{0.5}$ for the current to reach one-half of its original value. $$i=i_0e^{-Rt/L}$$ $$0.5i_0=i_0e^{-R t_{0.5}/L}$$ $$ t_{0.5}=(L/R)ln2$$ In the situation described here, the resistance R is increasing as the magnet loses more and more of its superconducting ability, so the time $t_{0.5}$ will be shorter.
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