Q. We have two wires $A$ and $B$ of same mass and same material. The diameter of the wire $A$ is half of that $B.$ If the resistance of wire $A$ is $24\ ohm$ then the resistance of wire $B$ will be
A) $12\ Ohm$
B) $3.0\ Ohm$
C) $1.5\ Ohm$
D) None of the above
Explanation
(c) Same mass, same material $i.e.$ volume is same or $Al =$ constant
Also, $R = \rho\frac{l}{A} \Rightarrow \frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \frac{A_{2}}{A_{1}} = \left( \frac{A_{2}}{A_{1}} \right)^{2} = \left( \frac{d_{2}}{d_{1}} \right)^{4}$
$\Rightarrow \frac{24}{R_{2}} = \left( \frac{d}{d/2} \right)^{4} = 16 \Rightarrow R_{2} = 1.5\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.