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QJEEM24Ph3949: JEE Main 2024 Physics - Class 12 JEEM24Ph3949 Solution: Two wires and are made up of the same material and have the…

Two wires AA and BB are made up of the same material and have the same mass. Wire AA has radius of 2.0 mm2.0 \mathrm{~mm} and wire BB has radius of 4.0 mm4.0 \mathrm{~mm} . The resistance of wire BB is 2Ω2 \Omega . The resistance of wire AA is ________ Ω\Omega .

Step-by-Step Verified Solution

amp;R=ρIA=ρVA2amp; and πr12I1=πr22I2amp;A1I1=A2I2amp; So R1R2=(A2A1)2amp;⇒R2=(r2r1)4amp;⇒R=32\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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