In a potentiometer experiment, the balancing length with a cell is $250 \, cm$. On shunting the cell with a resistance of $2 \, \Omega$, the balancing length becomes $125 \, cm$. The internal resistance of the cell is:

In a potentiometer,a balance point is obtained when:

While doing an experiment with a potentiometer as shown in the figure,it was found that the deflection is one-sided and $(i)$ the deflection decreased while moving the jockey from one end $A$ of the wire to the end $B$; $(ii)$ the deflection increased while the jockey was moved towards the end $B$.
$(i)$ Which terminal ($+$ or $-ve$) of the cell $E_1$ is connected at $X$ in case $(i)$ and how is $E_1$ related to $E$?
$(ii)$ Which terminal of the cell $E_1$ is connected at $X$ in case $(ii)$?

$A$ potentiometer wire of length $1\,m$ and resistance $10\,\Omega$ is connected in series with a cell of $emf$ $2\,V$ with internal resistance $1\,\Omega$ and a resistance box including a resistance $R$. If the potential difference between the ends of the wire is $1\,mV$,the value of $R$ is ............. $\Omega$.

In a potentiometer circuit,a cell of $2\,V$ $e.m.f.$ and $5\,\Omega$ internal resistance is connected to a uniform wire of length $1000\,cm$ and resistance $15\,\Omega$. The potential gradient of the wire is:

$A$ null point is found at $200\,cm$ in a potentiometer when the cell in the secondary circuit is shunted by $5\,\Omega$. When a resistance of $15\,\Omega$ is used for shunting,the null point moves to $300\,cm$. The internal resistance of the cell is $..............\,\Omega$.