$AB$ is a potentiometer wire of length $100 \mathrm{cm}$. When a cell ${\xi }_2$ is connected across $AC$, where $AC=75 \mathrm{cm}$, no current flows from ${\xi }_2$. Find emf of the cell ${\xi }_2$. The internal resistance of the cell ${\xi }_1$ is negligible.

 

A standard cell of emf $1.08 \mathrm{V}$ is balanced by the potential difference across $91 \mathrm{cm}$ of a metre-long wire supplied by a cell of emf $2 \mathrm{V}$ through a series resistor of resistance $2 \mathrm{\Omega }$. The internal resistance of the cell is zero. Find the resistance per unit length of the potentiometer wire.

Potentiometer wire $PQ$ of $1 \mathrm{m}$ length is connected to a standard cell ${\xi }_1$. Another cell ${\xi }_2$, of emf $1.02 \mathrm{V}$ is connected as shown in the circuit diagram with a resistance ‘$r$’ and a switch, $S$. With switch $S$ open, null position is obtained at a distance of $51 \mathrm{cm}$ from $P$. Calculate potential gradient of the potentiometer wire.

Potentiometer wire $PQ$ of $1 \mathrm{m}$ length is connected to a standard cell ${\xi }_1$. Another cell ${\xi }_2$, of emf $1.02 \mathrm{V}$ is connected as shown in the circuit diagram with a resistance ‘$r$’ and a switch, $S$. With switch $S$ open, null position is obtained at a distance of $51 \mathrm{cm}$ from $P$. Calculate the emf of the cell ${\xi }_1$.

Potentiometer wire $PQ$ of $1 \mathrm{m}$ length is connected to a standard cell ${\xi }_1$. Another cell ${\xi }_2$, of emf $1.02 \mathrm{V}$ is connected as shown in the circuit diagram with a resistance ‘$r$’ and a switch, $S$. With switch $S$ open, null position is obtained at a distance of $51 \mathrm{cm}$ from $P$. When switch $S$ is closed, will null point move towards $P$ or towards $Q$? Give reason.

A battery ${\xi }_1$ of $4 \mathrm{V}$ and a variable resistance $R_h$ are connected in series with the wire $AB$ of the potentiometer. The length of the wire of the potentiometer is $1$ metre. When a cell ${\xi }_2$ of emf $1.5$ volt is connected between points $A$ and $C$, no current flows through ${\xi }_2$.

Length of $AC=60 \mathrm{cm}$

Find the potential difference between the ends $A$ and $B$ of the potentiometer.

A battery ${\xi }_1$ of $4 \mathrm{V}$ and a variable resistance $R_h$ are connected in series with the wire $AB$ of the potentiometer. The length of the wire of the potentiometer is $1$ metre. When a cell ${\xi }_2$ of emf $1.5$ volt is connected between points $A$ and $C$, no current flows through ${\xi }_2$.

Length of $AC=60 \mathrm{cm}$

Would the method work, if the battery ${\xi }_1$ is replaced by a cell of emf of $1 \mathrm{V}$?