The $e.m.f.$ of a standard cell balances across $150 \ cm$ length of a potentiometer wire. When a resistance of $2 \ \Omega$ is connected as a shunt across the cell,the balance point is obtained at $100 \ cm$. The internal resistance of the cell is .............. $\Omega$.

In a potentiometer arrangement,a cell of $emf$ $1.25\,V$ gives a balance point at $35.0\,cm$ length of the wire. If the cell is replaced by another cell and the balance point shifts to $63.0\,cm,$ the $emf$ of the second cell is ............... $V$.

In the given potentiometer circuit,the length of the wire $AB$ is $3 \, m$ and its resistance is $R = 4.5 \, \Omega$. The length $AC$ for no deflection in the galvanometer is ............... $m$.

$A$ potentiometer wire is $4 \text{ m}$ long and a potential difference of $3 \text{ V}$ is maintained between the ends. The e.m.f. of the cell which balances against a length of $100 \text{ cm}$ of the potentiometer wire is: (in $\text{ V}$)

The figure shows a potentiometer wire $AB$ having a resistance of $5 \text{ } \Omega$ and a length of $10 \text{ m}$. The e.m.f. of the battery in the primary circuit is $5 \text{ V}$ and the external resistance is $45 \text{ } \Omega$. If the e.m.f. of the cell in the secondary circuit is $0.4 \text{ V}$, find the balancing length $AP$. (Internal resistance is negligible) (in $\text{ m}$)

The length of a potentiometer wire is $L$. $A$ cell of e.m.f. $E$ is balanced at a length $\frac{L}{5}$ from the positive end of the wire. If the length of the wire is increased by $\frac{L}{2}$,the same cell will give a balance point at distance $x$. The value of $x$ is