Question

Two wires of different materials, the length of the first is double the length of the second, and the radius of the second is double the radius of the first. The resistance of the first is equal to the resistance of the second . What is the ratio between the Resistivity of these two materials? ​

Answer 1

The ratio of the resistivities of two wires with equal resistance but differing dimensions is 1/4. This means that the resistivity of the first material is one fourth the resistivity of the second material.

Step-by-step explanation:

We need to find the ratio of the resistivities of two different materials. Given that the resistance of both wires is the same, we can use the formula for resistance of a cylindrical conductor, which is R = ρ(L/A) where R is resistance, ρ is resistivity, L is the length of the wire, and A is the cross-sectional area.

For the first wire (Material 1), let's assume a length of L and a radius of r. For the second wire (Material 2), the length is L/2 and the radius is 2r. The area is given by πr², so the cross-sectional area for the first wire is πr² and for the second wire is π(2r)².

Setting the resistances equal to each other, we have:
ρ₁(L/πr²) = ρ₂((L/2)/(π(2r)²)) Simplify to find the ratio of the resistivities (ρ₁/ρ₂) = 1/4. Thus, the resistivity of Material 1 is one fourth the resistivity of Material 2.