JEE MAIN - Physics (2024 - 4th April Evening Shift - No. 28)
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 ________ $$\Omega$$.
Answer
32
Explanation
$$\begin{aligned}
& R=\rho \frac{I}{A}=\rho \frac{V}{A^2} \\
& \text { and } \pi r_1^2 I_1=\pi r_2^2 I_2 \\
& A_1 I_1=A_2 I_2 \\
& \text { So } \frac{R_1}{R_2}=\left(\frac{A_2}{A_1}\right)^2 \\
& \Rightarrow \frac{R}{2}=\left(\frac{r_2}{r_1}\right)^4 \\
& \Rightarrow R=32
\end{aligned}$$
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