Two wires are made of the same material. Wire 1 has length that is 1.35 times the length of wire 2 and diameter that is 0.91 times the diameter of wire 2. What is the ratio of the resistance of wire 1 to the resistance of wire 2

1.117935:1

Explanation:

Since the wires are of the same material, they will have the same resistivity .

The cross-sectional area of the of a wire is given by;

where d is the diameter of the wire.

Also, the relationship between resistance R, cross-sectional area A and length l of a wire is given as follows;

Since the resistivity same for both wires, say wire 1 and wire 2, we can wreite the following;

Hence from eqaution (3), the ration of wire 1 to 2 is expressed as;

Given;

We then use equation (1) to fine the ratio of the area to

bearing in mind that

This ratio gives 0.8281. Substituting this into equation (5), we get the following;