If a wire of resistance R is melted and recasted to half

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If a wire of resistance R is melted and recasted to half of its length, then the new resistance of the wire will be

1. R / 4
2. R / 2
3. R
4. 2R

Correct Option: A

Initial resistance (R₁) = R; Initial length l₁is 1and final length (l₂) = 0.5 l . Volume of a wire = l . A. Since the volume of the wire remains the same after recasting, therefore l₁. A₁ = l₂ A₂

We also know that resistance of a wire (R)

R = ρ ×	l	.; R ∝	l
	A		A

∴	R₁	=	l₁	×	A₂	=	l	× 2 = 4
	R₂		l₂		A₁		0.5l

or, R₂ =	R₁	=	R
	4		4

[Alt : When wires are drawn from same volume but with different area of cross-section, then

R ∝	1
	(Area of cross-section)²