Uttar Pradesh Board-2018

If $\mathrm{R}$ is the resistance of each side and that of galvanometer of a balanced Wheatstone bridge; then total resistance across the terminals connecting the battery is 

A potentiometer wire $\mathrm{PQ}$ of $1 \mathrm{m}$ length is connected to a standard cell ${\mathrm{E}}_1$. Another cell ${\mathrm{E}}_2$ of $\mathrm{emf}$ $1.02 \mathrm{V}$ is connected as shown in the circuit diagram, with a resistor $\mathrm{R}$ and a switch $\mathrm{S}$. With switch $\mathrm{S}$ open, null point is obtained at a distance of $51 \mathrm{cm}$ from $\mathrm{P}$.

Calculate $\left(\mathrm{i}\right)$ the potential gradient of the potentiometer wire

A potentiometer wire $\mathrm{PQ}$ of $1 \mathrm{m}$ length is connected to a standard cell ${\mathrm{E}}_1$. Another cell ${\mathrm{E}}_2$ of $\mathrm{emf}$ $1.02 \mathrm{V}$ is connected as shown in the circuit diagram, with a resistor $\mathrm{R}$ and a switch $\mathrm{S}$. With switch $\mathrm{S}$ open, null point is obtained at a distance of $51 \mathrm{cm}$ from $\mathrm{P}$.

Calculate $\left(\mathrm{ii}\right)$ the $\mathrm{emf}$ of the cell ${\mathrm{E}}_1$

A potentiometer wire $\mathrm{PQ}$ of $1 \mathrm{m}$ length is connected to a standard cell ${\mathrm{E}}_1$. Another cell ${\mathrm{E}}_2$ of $\mathrm{emf}$ $1.02 \mathrm{V}$ is connected as shown in the circuit diagram, with a resistor $\mathrm{R}$ and a switch $\mathrm{S}$. With switch $\mathrm{S}$ open, null point is obtained at a distance of $51 \mathrm{cm}$ from $\mathrm{P}$.

Calculate $\left(\mathrm{iii}\right)$ when switch $\mathrm{S}$ is closed will null point shift towards $\mathrm{P}$ or $\mathrm{Q}$. Justify your answer.

What is the principle of a potentiometer ? The resistance of a potentiometer wire is $8 \mathrm{\Omega }$. Find the potential difference across the $4\mathrm{\Omega }$ resistor, when the sliding jockey is just in contact at the mid-point $\mathrm{C}$of the potentiometer wire :

Find out the reading of voltmeter with the help of the given electrical circuit.

A cell of internal resistance $\mathrm{r}$ passes current for some time in a resistor ${\mathrm{R}}_1$, in another resistance ${\mathrm{R}}_2$ current is passed for the same time. If same heat is produced in the two resistors them show that $\mathrm{r}=\sqrt{{\mathrm{R}}_1{\mathrm{R}}_2}$.

The length of a wire becomes three times by stretching it. The wire is connected with a source of constant voltage. What would be the effect on

$\left(\mathrm{iii}\right)$ drift speed of the free electrons of the wire?