Answer to Question #171843 in Electricity and Magnetism for loys

Question

wires a and b are made for 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

$R=\frac{\rho l}{S}=\frac{4 \rho l}{\pi d^2},$

$l_a=l_b,~\rho_a=\rho _b,~d_a=3d_b,$

$R\sim \frac{1}{d^2},$

$R_b=R_a\cdot(\frac{d_a}{d_b})^2=12\cdot 3^2=108~\Omega.$