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

NCERT Class XII
Physics - Exemplar Problems

Chapter 3. Current Electricity

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Answers

2015-06-12T19:10:39+05:30
Area of cross-section of A=π(d/2)²
                                      =1/4π mm²
Area of cross-section of B=π(2/2)² - π(1/2)²
                                      =π(1-1/4)
                                      =3/4π
We know, R = ρ*l/A
₀°₀ R(A) = ρ*l/(1/4π) = ρ*4πl
And, R(B) = ρ*l(3/4π) = ρ*4/3*πl
₀⁰₀R(A)/R(B) = ρ*4πl/ρ*4/3*πl = 4/(4/3) = 12/4 = 3
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