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 $24 \,ohm$, then the resistance of wire $B$ will be

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

Answer 1

Answer: (C)

Same mass, same material, i.e., volume is the same or $A l=$ 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$