Two conductors are made of the same material

Question:

 Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1 mm. Conductor B is a hollow tube of outer diameter 2 mm and inner diameter 1 mm. Find the ratio of resistance RA to RB.

Solution:

Resistance of wire R = ρ l/A

Where A is the cross-sectional area of the conductor

L is the length of the conductor

ρ is the specific resistance

RA = ρl/π(10-3 × 0.5)2

RB = ρl/ π[10-3)2 × (0.5 × 10-3)2]

Therefore, the ratio is RA/RB = 3:1

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