A potentiometer wire $AB$ having length $L$ and resistance $12\, r$ is joined to a cell $D$ of $emf$ $\varepsilon $ and internal resistance $r$. A cell $C$ having $emf$ $\varepsilon /2$ and internal resistance $3r$ is connected. The length $AJ$ at which the galvanometer as shown in figure shows no deflection is
JEE MAIN 2019, Medium
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$V_{A J}=I R_{A J}$
$\frac{E}{3}=\left(\frac{E}{12 r+3 r}\right) \times\left(\frac{x}{L} \times 12 r\right)$
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