The figure below shows three cylindrical copper conductors along with their face areas and lengths. Compare the
resistance and the resistivity of the three conductors. Justify your answer.

The figure below shows three cylindrical copper conductors along with their face areas and lengths. Compare the resistance and the resistivity of the three conductors. Justify your answer. 3L

Dear Student,

Here,

Case 1 

Length of the wire (L) = L

Resistance (R) = R₁

Area of cross section (A) = A

We have by the formula for resistivity

R₁ = ρ(L/A)

Case 2,

Length of the wire (L) = L

Resistance (R) = R₂

Area of cross section (A) = A

R₂ = ρ(3L/A/3)
 = ρ(3L/A) x 3
9ρ(L/A)
= 9R₁



Case 3,

Length of the wire (L) = L/3

Resistance (R) = R₃

Area of cross section (A) = 3A

R3 = ρ(L/3/3A)
 = ρ(L/3) x 1/3A
= 1/9ρ(L/A)
= 1/9 R₁

So, in all these cases the Resistance will change as R_1, R₂ (9R₁) and R₃ (1/9 R₁)

R₂ > R₁ > R₃

Also as it is of same material the resistivity remains same.



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