If a wire of resistance R is melted and recast to half of

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If a wire of resistance R is melted and recast to half of its length, then the new resistance of the wire will be

1. R
  4
2. R
  4
3. R
4. 2R

Correct Option: A

Let the original length be L; area of cross-section be A; and the resistivity be ?.
So, R = ?L/A
When the wire is melted and length is made half, i.e.
L/ = L/2, the area of cross-section A/ is such that,
AL = A/L/ (volume of the wire remains constant)
=> AL = A/(L/2)
=> A/ = 2A
Now, the new resistance is,
R/ = ?L//A/ = ?(L/2)/(2A)
=> R/ = R/4
Thus, the new resistance is one-fourth of the original resistance.