$A$ $6\,V$ 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 potentiometer experiments,two cells of e.m.f. $E_1$ and $E_2$ are connected in series $(E_1 > E_2)$,the balancing length is $64 \ cm$ of the wire. If the polarity of $E_2$ is reversed,the balancing length becomes $32 \ cm$. The ratio $E_1 / E_2$ is

$A$ $10 \,m$ long potentiometer wire is connected to a battery having a steady voltage. $A$ Leclanche cell is balanced at $4 \,m$ length of the wire. If the length is kept the same,but its cross-section is doubled,the null point will be obtained at ........... $m$.

$A$ potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery,used across the potentiometer wire,has an $EMF$ of $2.0\,V$ and a negligible internal resistance. The potentiometer wire itself is $4\,m$ long. When the resistance $R$,connected across the given cell,has values of $(i)$ infinity and $(ii)$ $9.5\,\Omega$,the balancing lengths on the potentiometer wire are found to be $3\,m$ and $2.85\,m$,respectively. The value of internal resistance of the cell is ............... $\Omega$.

$A$ potentiometer wire has a length of $100 \ cm$ and is connected to a cell of $emf \ E$. It is used to measure the $emf \ E_0$ of a battery with an internal resistance of $0.5 \ \Omega$. If the balance point is obtained at a distance of $\ell = 30 \ cm$ from the positive terminal,the $emf \ E_0$ of the battery is:

$A$ potentiometer wire has length $10\, m$ and resistance $10\, \Omega$. It is connected to a battery of $EMF$ $11\, V$ and internal resistance $1\, \Omega$. The potential gradient in the wire is ............... $V/m$.