Suppose you wish to fabricate a uniform wire from a mass m of a metal with density rhom and resistivity rho. if the wire is to have a resistance of r and all the metal is to be used, what must be the length and the diameter of this wire? (use any variable or symbol stated above as necessary.

Explanation:

Resistivity and resistance are proportional and depends of the length and the cross-sectional area of the wire:

furthermore, the density is the mass divided by the volume, and the volume can be written as the area multiplyed by the length:

Now you have tw equations and two variables, so you can solve for each of them.

first, solve for A in both equations and replace them:

now replace this into any of the previous equiations:

If you assume the wire has circular cross-sectional area, then the area is:

solving for d:

replacing A and simplifying:

answer; /// the above statement is (true);

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.