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
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Answer:
R/16
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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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