Answer
The correct answer is:
(d) 1/2 as much
Work Step by Step
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
