Question

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There are two conductors A and B of the same material, having lengths "l" and "2l"; and having radii r
and r/2 respectively. What is the ratio of their resistance?

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Answer 1

Answer:1:8

Explanation:. Resistance for a material

R varies length(l)

R varies 1/area(A)

Hence R=constant ×l/A

Constant depends on the material.let it k.

R1=(k1×l)/(π×r^2)

R2=(k2×2l)/[π×(r/2)^2]

R2=k2×8l/πr^2

R1:R2=k1×l/πr^2:k2×8l/πr^2

Since the material is same ..so k1=k2

R1:R2= 1:8

Answer 2

Answer: 1:8

Explanation:

Constant depends on the material. Let it be k.

R1=(k1×l)/(π×r^2)

R2=(k2×2l)/[π×(r/2)^2]

R2=k2×8l/πr^2

=>R1:R2=k1×l/πr^2:k2×8l/πr^2

Considering the same material, resistivity is same too

R1:R2= 1:8

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