Question

We have two wires $A$ and $B$ of the same mass and the same material. The diameter of the wire $A$ is half of that $B$. If the resistance of wire $A$ is $24ohm$, then the resistance of wire $B$ will be

• A. 12 ohm
• B. 3.0 ohm
• C. 1.5 ohm
• D. none of the above

Answer 1

Answer: (C)

Same mass, same material, i.e., volume is the same or $Al=$ constant
Also, $R=\rho \frac{l}{A}$
$\Rightarrow \frac{R_1}{R_2}=\frac{l_1}{l_2}\times \frac{A_2}{A_1}$
$={\left(\frac{A_2}{A_1}\right)}^2={\left(\frac{d_2}{d_1}\right)}^4$
$\Rightarrow \frac{24}{R_2}={\left(\frac{d}{d/2}\right)}^4=16$
$\Rightarrow R_1=1.5\Omega$