Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1.0 mm. Conductor B is a hollow tube of outside diameter 2.7 mm and inside diameter 2.0 mm. What is the resistance ratio RA/RB, measured between their ends?

Since the conductors are made of the same material and length the product of the resistivity and length of the conductor are the same for both conductors and is constant.

R = ρL/A = constant / A

So RA = constant

And RaAa = RbAb

Ra/Rb= Ab/Aa

D = 1mm = 1×10‐³m

Aa = πD²/4 = π(1×10-³)²/4 = 7.85×10-⁷ m²

D1 = inner diameter of conductor B = 2.0mm = 2×10-³m

D2 = outer diameter of conductor B = 2.7mm = 2.7×10-³m

Ab = π(D2²-D1²)/4 = π((2.7×10-³)²-(2.0×10-³)²)/4 = 2.58×10-⁶m²

So,

Ra/Rb= Ab/Aa = 2.58×10-⁶/7.85×10-⁷ = 3.23

The resistance ratio is 3.23. This makes sense because a larger cross sectional area means more electrons can flow through the conductor per time and so lesser resistance. Conductor B has a larger cross sectional area and so lesser resistance when compared to conductor A.