Question

If a₁ and a₂ are the area of cross-sections of the two conductors of length 'l' each, such that R₁ and R₂ are their electrical resistance derive a relationship between R₁, R₂, a₁ and a₂.

Answer 1

For two conductors made of the same material and having the same length l, resistance is inversely proportional to the area of cross-section:

`R ∝ 1/a`

Using the relation `R = ρl/a`: `R_1 = ρl/a_1` and `R_2 = ρl/a_2`

Dividing the two equations:

`R_1/R_2 = (ρl/a_1)/(ρl/a_2) = a_2/a_1`

Therefore, the required relationship is:

`R_1/R_2 = a_2/a_1`

Equivalently, R₁a₁ = R₂a₂.

So, for conductors of equal length made of the same material, their resistances are in the inverse ratio of their areas of cross-section.