In a potentiometer experiment,a cell is balanced at a length of $240 \ cm$. When the cell is shunted with a resistance of $2 \ \Omega$,it is balanced at a length of $120 \ cm$. The internal resistance of the cell is .......... $\Omega$.

$A$ potentiometer wire,$10 \, m$ long,has a resistance of $40 \, \Omega$. It is connected in series with a resistance box and a $2 \, V$ storage cell. If the potential gradient along the wire is $0.1 \, mV/cm$,the resistance unplugged in the box is .............. $\Omega$.

$A$ $6\,V$ battery is connected to the terminals of a $3\,m$ long uniform wire having resistance $100\,\Omega$. The difference in potential between two points on the wire separated by a distance of $50\,cm$ will be ............. $V$.

In a potentiometer,a balance point is obtained when:

In a potentiometer experiment,cells of e.m.f. $E_1$ and $E_2$ are connected in series $(E_1 > E_2)$ and the balancing length is $80 \ cm$. If the polarity of $E_2$ is reversed,the balancing length becomes $20 \ cm$. The ratio $E_1 / E_2$ is:

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