Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 26 - Current and Resistance - Questions - Page 764: 1

Answer

We can rank them according to their end to end resistances: $A = B = C \gt (A+B) = (B+C) \gt (A+B+C)$

Work Step by Step

$R = \frac{\rho~L}{A}$ Since the conductors are made of the same material, the conductivity $\rho$ is the same for all three conductors. Also, it is given that the three conductors have the same length $L$ We can write an expression for the resistance of each of the given options: $A$: $R = \frac{\rho~L}{A} = \frac{\rho~L}{3l^2-2l^2} = \frac{\rho~L}{l^2}$ $B$: $R = \frac{\rho~L}{A} = \frac{\rho~L}{2l^2-l^2} = \frac{\rho~L}{l^2}$ $C$: $R = \frac{\rho~L}{A} = \frac{\rho~L}{l^2}$ $A+B$: $R = \frac{\rho~L}{A} = \frac{\rho~L}{3l^2-l^2} = \frac{1}{2}\cdot \frac{\rho~L}{l^2}$ $B+C$: $R = \frac{\rho~L}{A} = \frac{\rho~L}{2l^2} = \frac{1}{2}\cdot \frac{\rho~L}{l^2}$ $A+B+C$: $R = \frac{\rho~L}{A} = \frac{\rho~L}{3l^2} = \frac{1}{3}\cdot \frac{\rho~L}{l^2}$ We can rank them according to their end to end resistances: $A = B = C \gt (A+B) = (B+C) \gt (A+B+C)$
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