Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 30 - Current and Resistance - Conceptual Questions - Page 886: 11

Answer

We can rank the resistances in order from largest to smallest: $R_d \gt R_a = R_e \gt R_c \gt R_b$

Work Step by Step

We can write a general expression for the resistance $R_0$: $R_0 = \frac{\rho~L}{A} = \frac{\rho~L}{\pi~r^2}$ We can write an expression for the resistance in each case: (a) $R_a = \frac{\rho~L}{\pi~r^2} = R_0$ (b) $R_b = \frac{\rho~L}{\pi~(2r)^2} = \frac{1}{4} \times R_0$ (c) $R_c = \frac{\rho~(2L)}{\pi~(2r)^2} = \frac{1}{2} \times R_0$ (d) $R_d = \frac{\rho~(2L)}{\pi~r^2} = 2 \times R_0$ (e) $R_e = \frac{\rho~(4L)}{\pi~(2r)^2} = R_0$ We can rank the resistances in order from largest to smallest: $R_d \gt R_a = R_e \gt R_c \gt R_b$
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