PYQ NEET- Current Electricity L-1

Question: 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: (2023)#

A) $81 \Omega$

B) $9 \Omega$

C) $729 \Omega$

D) $243 \Omega$

Answer: $9 \Omega$#

Explanation#

$\mathrm{R}=\frac{\rho \mathrm{L}}{\mathrm{A}}$

If diameter becomes thrice then cross section area will become 9 times so

$\mathrm{R} \propto \frac{1}{\mathrm{~A}}$

Resistance will become $\frac{1}{9}$ times

$\mathrm{R}^{\prime}=\frac{81 \Omega}{9}=9 \Omega$