Answer
$i = 2.97~mA$
Work Step by Step
We can find the current in the wire:
$i = \frac{V}{R}$
$i = \frac{V}{\rho~L/A}$
$i = \frac{V~A}{\rho~L}$
$i = \frac{V~\pi~r^2}{\rho~L}$
$i = \frac{(12.0\times 10^{-6}~V)~(\pi)~(2.00\times 10^{-3}~m)^2}{(1.69\times 10^{-8}~\Omega\cdot m)~(3.00~m)}$
$i = 2.97\times 10^{-3}~A$
$i = 2.97~mA$
