Question

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 :

• A. $\frac{5}{12}$ L
• B. $\frac{11}{24}$ L
• C. $\frac{11}{12}$ L
• D. $\frac{13}{24}$ L

Answer 1

Answer: (D)

$\frac{13}{24}$ L

Answer 2

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