Acommon cylindrical copper wire used in a lab is 841 m long. find the radius (in mm) of a wire necessary to have 0.5 ohms of resistance. (the resistivity of copper at room temperature is 1.68×10-8  ohm × meter). express the answer  (only numerical value) to one decimal place.

The relationship between the resistance R of a wire and its resistivity  is given by

where L is the length of the wire and A is its cross sectional area.

In the problem, we have ,  and . So we can solve the find the area A:


For a cylindrical wire, the cross sectional area is given by

where r is the radius. We know the value of the area A, so now we can find the radius of the wire: