Question

A uniform wire of resistancee 100Ω is melted and recast into wire of length double that of theoriginal. What would be the resistance of the new wire formed?

Answer 1

A uniform wire of resistance 100Ω is melted and recast into wire of length double that of the original.

so, volume of wire remains constant.let V.

we know, R = ρl/A

or, R = (ρl × l)/(A × l) = ρl²/V

[ where V = Al , volume = cross sectional area × length ]

now, R is directly proportional to square of length.

i.e., R1/R2 = l1²/l2²

here, R1 = 100Ω, l1 = l and l2 = 2l

so, (100)/R2 = l²/(2l)² = 1/4

or, R2 = 100 × 4 = 400 Ω

hence, new resistance of wire will be 400Ω.