In the figure, the potentiometer wire $AB$ of length $L$ and resistance $9r$ is joined to the cell $D$ of $emf$ $\varepsilon $ and internal resistance $r$. The cell $C's$ $emf$ is $\frac{\varepsilon }{2}$and its internal resistance is $2r$. The galvanometer $G$ will show no deflection when the length $AJ$ is
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Potential gradient $(\mathrm{x})=\frac{\mathrm{IR}}{\mathrm{L}}$
$\quad=\frac{\varepsilon}{10 \mathrm{r}} \frac{9 \mathrm{r}}{\mathrm{L}}$
$=\frac{9 \varepsilon}{10 L}$
$\because \frac{\varepsilon}{2}=\mathrm{x} \times \ell_{\mathrm{AJ}}$
$C_{\mathrm{AJ}}=\frac{\varepsilon}{2} \times \frac{10 \mathrm{L}}{9 \varepsilon}=\frac{5 \mathrm{L}}{9}$
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