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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.
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Solution
We know that the resistance of wire is `R = ρ l/A` where A is cross-sectional area of conductor and ρ is the specific resistance or resistivity and L is the length of conductor.
The resistance of first conductor
`R_A = (ρl)/(pi(10^-3 xx 0.5)^2`
The resistance of second conductor,
`R_B = (ρl)/(pi[(10^-3)^2 - (0.5 xx 10^-3)^2]`
Now, the ratio of two resistors is given by
`R_A/R_B = ((10^-3)^2 - (0.5 xx 10^-3)^2)/(0.5 xx 10^-3)^2` = 3:1
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