$AB$ is a potentiometer wire of length $100\, cm$ and its resistance is $10\,\Omega$. It is connected in series with a resistance $R = 40\,\Omega$ and a battery of $e.m.f.$ $2\,V$ and negligible internal resistance. If a source of unknown $e.m.f.$ $E$ is balanced by $40\, cm$ length of the potentiometer wire,the value of $E$ is ................. $V$. (in $,V$)

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

When a potentiometer is connected between the points $A$ and $B$ as shown in the circuit,the balance point is obtained at $64 \ cm$. When it is connected between $A$ and $C$,the balance point is $8 \ cm$. If the potentiometer is connected between $B$ and $C$,the balance point will be: (in $cm$)

$A$ $2\,V$ battery,a $15\,\Omega$ resistor,and a potentiometer of $100\,cm$ length are all connected in series. If the resistance of the potentiometer wire is $5\,\Omega$,then the potential gradient of the potentiometer wire is ............... $V/cm$.

The figure shows a $2.0 \; V$ potentiometer used for the determination of internal resistance of a $1.5 \; V$ cell. The balance point of the cell in open circuit is $76.3 \; cm$. When a resistor of $9.5 \; \Omega$ is used in the external circuit of the cell,the balance point shifts to $64.8 \; cm$ length of the potentiometer wire. Determine the internal resistance (in $\Omega$) of the cell.

The length of a potentiometer wire is $l$. $A$ cell of $emf$ $E$ is balanced at a length $l/3$ from the positive end of the wire. If the length of the wire is increased by $l/2$,at what distance will the same cell give a balance point?