## College Physics (4th Edition)

We can write an expression for the resistance of a wire: $R = \frac{\rho~L}{A} = \frac{\rho~L}{\pi~r^2}$ We can write an expression for the original resistance: $R_1 = \frac{\rho~L_1}{\pi~r_1^2}$ We can find an expression for the final resistance: $R_2 = \frac{\rho~L_2}{\pi~r_2^2}$ $R_2 = \frac{\rho~(2~L_1)}{\pi~(2~r_1)^2}$ $R_2 = \frac{2~\rho~L_1}{4~\pi~r_1^2}$ $R_2 = \frac{1}{2}~\frac{\rho~L_1}{\pi~r_1^2}$ $R_2 = \frac{1}{2}~R_1$ The correct answer is: (d) 1/2 as much