Question

two cylindrical wires of the same material have their lengths in the ratio of 4:9 what should be the ratio of their radii so that their resistance are in the ratio of 4:1

Answer 1

Given:

Ratio of lengths of wires, i.e., l₁ : l₂ = 4 : 9

Ratio of resistance of wires, i.e., R₁ : R₂ = 4 : 1

To Find:

Ratio of radii of wires, i.e., r₁ : r₂

Calculation:

- It is given that

R₁ / R₂ = 4 / 1

⇒ (ρl₁/A₁) / (ρl₂/A₂) = 4 / 1

⇒ (l₁ / l₂) × (A₂ / A₁) = 4 / 1

⇒ (4 / 9) × (πr₂² / πr₁²) = 4 / 1

⇒ (r₂ / r₁)² = 9

⇒ (r₂ / r₁) = √9

⇒ (r₂ / r₁) = 3

⇒ r₁ / r₂ = 1 / 3

- Hence, the ratio of their radii is 1 : 3

Answer 2

Answer:Ratio of raddi is 1:3 i.e. r1:r2

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