The resistance of a wire of uniform diameter D and length L is R. The resistance of another wire of the same
material but diameter 2 D and lengh 4 L will be?
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Answer:
R (same)
Explanation: Let the resistivity of the wire(material) be ρ.
As we know,
R = ρl/A , where l is length and A is area of circle(face).
Case 1 : Area of circle = πr² = π(D/2)²
∴ R = ρL/π(D/2)² = 4рL/πD²
Case 2 : Area of circle = πr² = π(2D/2)²
∴ R' = ρ(4L)/π(D)² = 4рL/πD²
R' = R
From both, resistance is equal/same.
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