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Q. If the length and area of cross-section of a conductor are doubled, then its resistance will be

AIIMSAIIMS 2014

Solution:

Initial length of the conductor
$l_{1}=l$
Final length of the conductor
$I_{2}=2 I$
Initial cross-sectional area $A_{1}=A$
Final cross-sectional area $A_{2}=2 A$
The resistance of conductors given by
$R=\rho \frac{1}{A} \propto \frac{1}{A}$
As both the length and area are doubled
Hence, there will be no change in the resistance of the conductor and so it will remain unchanged.