In the given potentiometer circuit length of the wire $AB$ is $3\mathrm{m}$ and resistance is $R=4.5\Omega$.  The length $AC$ for no deflection in galvanometer is 

A battery of  $\mathrm{emf}{E}_0=12 \mathrm{V}$ is connected across a $4\mathrm{m}$ long uniform wire having resistance $4\Omega /\mathrm{m}$. The cells of small emfs  ${\epsilon }_1=2\mathrm{V}$and ${\epsilon }_2=4\mathrm{V}$ having internal resistance $2\Omega$ and $6\Omega$ respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point $N$, the distance of point $N$ from the point $A$ is equal to

The net emf and internal resistance of three batteries as shown in figure is 

A conducting solid sphere is joined in an electrical circuit as shown in figure. Two imaginary points $A$ and $B$ are taken inside the sphere. For given conditions