Consider two cylindrical conductors made of the same ohmic material. v1 ~e1 i1 ℓ1 r1 b v2 ~e2 i2 ℓ2 r2 b if rho2 = rho1 , r2 = 2 r1 , ℓ2 = 2 ℓ1 , and v2 = v1 , find the ratio r2 r1 of the resistances

3/4

Explanation:

Here is the complete question

Consider two cylindrical conductors made of the same ohmic material. If ρ2 = ρ1 , r2 = 2 r1 , ℓ2 = 3 ℓ1 , and V2 = V1 , find the ratio R2 R1 of the resistances

Resistance, R = ρl/A where ρ = resistivity, l = length and A = area

For cylinder 1, R₁ = ρ₁l₁/A₁

For cylinder 2, R₂ = ρ₂l₂/A₂

ρ₂ = ρ₁, l₂ = 3l₁, r₂ = 2r₁  where r₁ and r₂ are the radii of the cylinders.

R₂/R₁ = ρ₂l₂/A₂ ÷ ρ₁l₁/A₁

        = ρ₂l₂A₁/ρ₁l₁A₂

        = ρ₂l₂πr₁²/ρ₁l₁πr₂²

        = ρ₂l₂r₁²/ρ₁l₁r₂²

substituting the required values

= ρ₁ × 3l₁ × r₁²/ρ₁ × l₁ × (2r₁)²

R₂/R₁ = 3/4