A cylindrical conductor of length 'l' and area of cross section 'A' has a resistance 'R'. Another conductor of length 2.5l and resistance 0.5R of the same material has area of cross section?

Answer: A₂ = 5A

Explanation:

L1 = L

A1 = A

R1 = R

R2 = 0.5R

L₂ = 2.5L

A2 = ?

from resistance formula,

R = ρL / A

but since they are of the same material,

ρ₁ = ρ₂ = ρ

R₁ = ρL₁ / A₂ ... equation i

R₂ = ρL₂ / A₂ ... equation ii

dividing equation ii by i,

R₂ / R₁ = (L₂ / A₂) / (L₁ / A₁) ... [ρ cancles out]

R₂ / R₁ = (L₂ * A₁) / (A₂ * L₁)

0.5R / R = (2.5L * A) / (A₂*L)

0.5 = 2.5A / A₂

A₂ = 2.5A / 0.5

A₂ = 5A

R = (ρ x l) / A [Resistance = resisitivity times length divided by area of cross-section]

0.5R = (ρ x 2.5l) / A'

0.5R/2.5 = (ρ x l) / A'

R/5 = (ρ x l) / A'

R = 5 (ρ x l) / A'

(ρ x l) / A = 5 (ρ x l) / A'

A' = 1/5 A

A' = 0.2 A