The circuit diagram shows the use of a potentiometer to measure a small emf produced by a thermocouple connected between $\mathrm{X}$ and $\mathrm{Y}$. The cell C, of emf $2 \mathrm{V}$, has negligible internal resistance. The potentiometer wire $\mathrm{PQ}$ is $1.00$ m long and has resistance $5\mathrm{\Omega }$. The balance point $\mathrm{S}$ is found to be $400 \mathrm{mm}$ from $\mathrm{P}$. Calculate the value of emf generated by the thermocouple.

A resistance of $\mathrm{R\Omega }$ draws current from a potentiometer. The potentiometer has a total resistance of ${\mathrm{R}}_0\mathrm{\Omega }$ (Fig. 3.303). A voltage $\mathrm{V}$ is supplied to the potentiometer. Derive an expression for the voltage across $\mathrm{R}$ when the sliding contact is in the middle of the potentiometer.

In the metre bridge experiment, a student observed a balanced point at the point J, where AJ $=\mathrm{l}$. Draw the equivalent Wheatstone bridge diagram for this set-up. (Fig.).

The values of $\mathrm{R}$ and $\mathrm{X}$ are both doubled and then interchanged. What would be the new position of the balance point? If, in this set-up, the galvanometer and battery are interchanged at the balance point position, how will the balance point get affected?

Write the condition of balance in Wheatstone bridge. In the given Wheatstone bridge, the current in the resistor $3\mathrm{R}$, is zero. Find the value of $\mathrm{R}$, if the carbon resistor, connected in one arm of the bridge, has the colour sequence of red, red and orange [Fig.]. The resistances, of $\mathrm{BC}$ and $\mathrm{CD}$ arms, are now interchanged and another carbon resistance $\mathrm{X}$ is connected in place of $\mathrm{R}$ so that the current through the arm $\mathrm{BD}$ is again zero. Write the sequence of colour bands of this carbon resistor. Also find the value of current through it.

A battery of internal resistance $\mathrm{r}\left(=4\mathrm{\Omega }\right)$ is connected to the network of resistances, as shown in Fig.  What must be the value of $\mathrm{R}$, so that maximum power is delivered to the network? What is the maximum power ?