Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1 m. Conductor B is a hollow tube of inside diameter 1 m and outside diameter 2 m. The ratio of their resistance, RA/RBRA/RB, is:

Ra / Rb = 3

Explanation:

The resistance is defined by the expression

         r = ρ L / A

where A is the area of ​​the wire and L is the length

let's find the area of ​​each wire

a) solid wire (A) of d₁ = 1 m

           r = d₁ / 2 = 0.5 m

          A = π r²

          A = π 0.5²

          R_a =

          R_a = 4 \frac{\rho \ L}{\pi   }

b) hollow tube (B) of d₁ = 1 m and d₂ = 2m

the radios are

            r₁ = 0.5 m

            r₂ = 1 m

the area is

            A = π r₂² - π r₁²

            A = π (r₂² - r₁²)

            A = π (1² - 0.5²)

            A = π 0.75

resistance is

             R_b =

             R_b = 1.33 \frac{ \rho \ L }{\pi  }

therefore the relationship between these two resistances is

             Ra / Rb = 4 / 1.33

             Ra / Rb = 3

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