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Question

If a metallic wire of resistance R is melted and recast to half of its length, the new resistance of the wire is ___.

A
R4
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B
R2
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C
R
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D
2R
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Solution

The correct option is A R4
Volume of the metallic wire = Length×Area of crosssection
If l and A are the original length and area of cross -section and l' and A' are their corresponding values on recasting.
Al=Alorll=AAll=12(Given)AA=12
New resistance, R=ρlA
As R=ρlA
RR=ρlAρlA
=(ll)(AA)
=(12)(12)=14
or R=R4

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