Question

A conductor of radius r, length l and resistivity rho has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the The resistance of the new conductor is

Answer 1

Answer:

R/16

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Answer 2

Resistance of the new conductor is  1/16 if length is reduced to 1/4

Explanation:

Radius = r

Length = l

resistivity = ρ

A = πr²

Resistance R =  ρ l/A   =  ρ l/ πr²

Volume = πr²l

Now new Length = l/4

Hence   πr²l   = πr²l/4

=> new Radius = 2r

A = π(2r)² = 4πr²

New resistance    = ρ (l/4)/4πr²

= (1/16) ρ l/ πr²

= R/16

resistance of the new conductor is  1/16  

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