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A certain wire A has resistance 81 $\Omega$. The resistance of another wire B of same material and equal length but of diameter thrice the diameter of A will be:
A
81 $\Omega$
B
9 $\Omega$
C
729 $\Omega$
D
243 $\Omega$
Detailed Solution
$R=\dfrac{\rho L}{A}$. If diameter becomes thrice, cross-sectional area becomes 9 times, so $R\propto\dfrac{1}{A}$ means resistance becomes $\dfrac{1}{9}$ times: $R'=\dfrac{81\ \Omega}{9}=9\ \Omega$.