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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
  • A$\frac{{11}}{{12}}\,L$
  • B$\frac{{11}}{{24}}\,L$
  • C$\frac{{13}}{{24}}\,L$
  • D$\frac{{5}}{{12}}\,L$
JEE MAIN 2019, Medium
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