Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 28 - Fundamentals of Circuits - Conceptual Questions - Page 789: 13

Answer

We can rank the values of the resistances from largest to smallest: $R_2 \gt R_3 \gt R_1$

Work Step by Step

We can write an expression for the voltage as a capacitor discharges: $V(t) = V_0~e^{-t/RC} = \frac{V_0}{e^{t/RC}}$ For larger values of $R$, the voltage will decrease more slowly. For smaller values of $R$, the voltage will decrease more quickly. We can see that the voltage decreases the most quickly for $R_1$, so it has the smallest resistance. We can see that the voltage decreases the most slowly for $R_2$, so it has the largest resistance. We can rank the values of the resistances from largest to smallest: $R_2 \gt R_3 \gt R_1$
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