Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0 \mathrm{~mm}$ and wire $B$ has radius of $4.0 \mathrm{~mm}$. The resistance of wire $B$ is $2 \Omega$. The resistance of wire $A$ is _____$\Omega$.

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Aicharya · Accepted Answer

$\begin{aligned} & \because \mathrm{R}=\frac{ho \ell}{\mathrm{A}}=\frac{ho \mathrm{V}}{\mathrm{A}^2} \ & 	herefore \frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}=\frac{\mathrm{A}_{\mathrm{B}}^2}{\mathrm{~A}_{\mathrm{A}}^2}=\frac{\mathrm{r}_{\mathrm{B}}^4}{\mathrm{r}_{\mathrm{A}}^4} \ & \Rightarrow \frac{\mathrm{R}_{\mathrm{A}}}{2}=\left[\frac{4 	imes 10^{-3}}{2 	imes 10^{-3}}ight]^4 \ & \Rightarrow \mathrm{R}_{\mathrm{A}}=32 \Omega .\end{aligned}$

Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0…

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