Q. 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 fig. shows no deflection is :

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Solution:

$i = \frac{\varepsilon}{13r} $
$ i\left(\frac{x}{L} 12r\right) = \frac{\varepsilon}{2} $
$ \frac{\varepsilon}{13r} \left[\frac{x}{L} .12r\right] = \frac{\varepsilon}{2} \Rightarrow x = \frac{13L}{24} $

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