Question

three cylindrical copper conductor along with their faces areas and length first conductors area is one in length is one second conductor area is 3 and length is 3 and third conductors length thing and area is 3 compare their Resistivity and resistance justify your answer

Answer 1

The required formula is R = ρL / A
where R = resistance through the material ; ρ = resistivity of the material ; L = length of the material ; A = cross sectional are of it.
PART 1(resistivity of all the 3 cylinders are same) :
For image (a); R₁ = ρ.L / A
For image (b); R₂ = ρ.(3L) / (A/3) = ρ.9L / A
For image (c); R₃ = ρ.(L/3) / (3.A) = ρ.L / 9.A
Therefore, R₁ : R₂ : R₃ = (ρ.L / A) : (ρ.9L / A) : (ρ.L / 9.A) = 1 : 9 :(1/9)
or, R₁ : R₂ : R₃ = 9 : 81 : 1
PART 2(in case those were made of different material, and resistance of all 3 are same) :
For image (a); R = ρ₁.L / A
or, ρ₁ = R.A / L
For image (b); R = ρ₂.(3L) / (A/3) = ρ.9L / A
or, ρ₂ = R.A / 9.L
For image (c); R = ρ₃.(L/3) / (3.A) = ρ₃.L / 9.A
or, ρ₃ = 9.R.A / L
Therefore, ρ₁ : ρ₂ : ρ₃ = (R.A / L) : (R.A / 9.L) : (9.R.A / L)
or, ρ₁ : ρ₂ : ρ₃ = 1 : (1/9) : 9 = 9 : 1 : 81

Answer 2

Hello writer, I checked your question which is from the chapter of physics .

I am going to give you a formula with help of which you can solve the question . Resistance R=R=p L/A where p-resistivity of the material,L-length, A-cross-sectional area.

I hope this formula will help you in find out the answer