$A$ cell balances against a length of $150 \ cm$ on a potentiometer wire when it is shunted by a resistance of $5 \ \Omega$. But when it is shunted by a resistance of $10 \ \Omega$,then the balancing length increases by $25 \ cm$. The balancing length when the cell is in an open circuit is: (in $cm$)

In the following circuit, a $10 \, m$ long potentiometer wire with resistance $1.2 \, \Omega/m$, a resistance $R_1$, and an accumulator of $emf$ $2 \, V$ are connected in series. When the $emf$ of the thermocouple is $2.4 \, mV$, the deflection in the galvanometer is zero at a balancing length of $5 \, m$. The current supplied by the accumulator is:

In the potentiometer experiment shown in the figure,for the position $X$ of the jockey $J$,there occurs a null deflection in the galvanometer. Then the potential difference between points $A$ and $X$ is ................ $V$.

If the length of the potentiometer wire is increased by keeping the potential difference across the wire constant,then:

Two cells $A$ and $B$ are connected in the secondary circuit of a potentiometer one at a time and the balancing lengths are respectively $360 \ cm$ and $420 \ cm$. If the emf of $A$ is $2.4 \ V$,the emf of the second cell $B$ is (in $V$)

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 $E_1$.