Question

Wires A and B are made of the same material and have the same length. However, the diameter of wire A is thrice the diameter of wire B. Wire A has a resistance of 12.0 ohms. What is the resistance of wire B?

Answer 1

Express the resistance of A and B in terms of area, resistivity, and length:

$$R_A=\frac{\rho L}{A_A}=\frac{4\rho L}{\pi d^2}=12\space\Omega,\\\space\\ R_B=\frac{\rho L}{A_B}=\frac{4(3^2)\rho L}{\pi d^2}=\frac{36\rho L}{\pi d^2}=\frac{9\rho L}{\pi d^2},\\\space\\ R_B=9·12=108\space\Omega.$$