Question

When a piece of aluminium wire of finite length is drawn through a series
of dies to reduce its diameter to half its original value, its resistance will
become (AIIMS 1997.MH-CET 2000,UPSEAT 2001.CBSE PMT 2​

Answer 1

=>  When a piece of aluminium wire of finite length is drawn through series of dies to reduce it's diameter to half it's original value, it's resistance will become sixteen times .

We know ,

• R= ρ l/A

where,

R  is resistance of wire  

ρ= resistivity of conductor

l= length of conductor

A= area of cross section  

so,

=> R= p V/A²

which implies R is inversely proportional to A²

=> R is inversely proportional to d⁴

=> Rα 1/d⁴

Hence,

d reduces to d/2

and  d⁴ reduces to d⁴/16 .

Therefore,

R=16R

Hence R increases 16 times more.

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