In the figure, the potentiometer wire $AB$ of length $L$ and resistance $9r$ is joined to the cell $D$ of $\mathrm{emf}$ $\varepsilon$ and internal resistance $r$. The cell $C’s$ $\mathrm{emf}$ is $\varepsilon /2$ and its internal resistance is $2r$. The galvanometer $G$ will show no deflection when the length $AJ$ is
  • A$\frac{{4L}}{9}$
  • B$\frac{{5L}}{9}$
  • C$\frac{{7L}}{{18}}$
  • D$\frac{{11L}}{{18}}$
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