In the Given Circuit ‘a’ is an.... | JEE Main 2022

JEE MAIN 2022

27-06-2022 S2

Question

In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be $\sqrt{\frac{x}{2}}$ . The value of x is _____ .

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Solution

$\begin{aligned} & \mathrm{R}=\left(\frac{\mathrm{ma}}{3}\right)+\left(\frac{\mathrm{a}}{2 \mathrm{~m}}\right) \\ & \frac{\mathrm{dR}}{\mathrm{dm}}=\frac{\mathrm{a}}{3}-\frac{\mathrm{a}}{2 \mathrm{~m}^2}=0 \\ & \frac{\mathrm{a}}{3}=\frac{\mathrm{a}}{2 \mathrm{~m}^2} \\ & \mathrm{~m}^2=\frac{3}{2} \\ & \mathrm{~m}=\sqrt{\frac{3}{2}} \\ & \mathrm{x}=3\end{aligned}$

Question Tags

JEE Main

Physics

Easy

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