Question

The resistance of uniform wire of lenght L and diameter d is R .The resistance of another wire of same material but lenght 4L and diamter 2d will be​

Answer 1

Answer :

For wire A :-

• Length : L
• Diameter : d (Radius : d/2)
• Resistance : R

For wire B :-

• Length : 4L
• Diameter : 2d (Radius : d)

We have to find resistance of wire B$.$

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◈ We know that, resistance of conductor is directly proportional to the length of conductor (R ∝ l) and inversely proportional to the area of cross section of conductor (R ∝ 1/A).

• R = ρ × l / A

ρ denotes resistivity of the conductor. ATQ, both wires are made up from same material so we can say that

⇒ ρ₁ = ρ₂

⇒ R₁ × l₁ / A₁ = R₂ × l₂ / A₂

⇒ R₁ × l₁ / (πr₁²) = R₂ × l₂ / (πr₂²)

⇒ 4RL/d² = 4R₂L/d²

⇒ R₂ = R