$A$ potentiometer has a potential gradient of $2 \, mV/cm$. It is used to measure the potential difference across a $10 \, \Omega$ resistor. If the length of the potentiometer wire required to obtain the null point is $50 \, cm$,the current flowing through the $10 \, \Omega$ resistor is ............. $mA$.

$A$ battery of $emf$ $E_0 = 12\, V$ is connected across a $4\,m$ long uniform wire having resistance $4\,\Omega /m$. The cells of small $emfs$ $\varepsilon_1 = 2\,V$ and $\varepsilon_2 = 4\,V$ having internal resistance $2\,\Omega$ and $6\,\Omega$ respectively,are connected in parallel as shown in the figure. If the galvanometer shows no deflection at point $N$,the distance of point $N$ from point $A$ is equal to:

$A$ cell is connected to a potentiometer, and the balance point is obtained at a length of $2 \, m$. When a resistance of $5 \, \Omega$ is connected in parallel with the cell, the balance point is obtained at a length of $3 \, m$. What is the internal resistance of the cell in $\Omega$?

The figure shows a simple potentiometer circuit for measuring a small $e.m.f.$ produced by a thermocouple. The potentiometer wire $PQ$ has a resistance of $5 \,\Omega$ and the driver cell has an $e.m.f.$ of $2 \, V$. If a balance point is obtained at $0.600 \, m$ along $PQ$ when measuring an $e.m.f.$ of $6.00 \, mV$,what is the value of resistance $R$ in $\Omega$?

Explain the comparison of the electromotive force (emf) of two cells using a potentiometer with a necessary diagram.

For the arrangement of the potentiometer shown in the figure,the balance point is obtained at a distance $75\,cm$ from $A$ when the key $k$ is open. The second balance point is obtained at $60\,cm$ from $A$ when the key $k$ is closed. Find the internal resistance (in $\Omega$) of the battery $E_1$.