Question

What is a potentiometer? Explain its principal.
(a). Explain how it can be used to compare the emf of two cells.
(b). Explain how it can be used to determine the internal resistance of a cell.

Answer 1

Hint: A potentiometer is a device which consists of a long potentiometer wire connected to a battery or known potential and the potential is distributed along the length of the wire. A potentiometer has various applications and it can be used to determine the emf or potential difference in a circuit.

Complete answer:
A potentiometer is an instrument containing a three-terminal resistor. It has a sliding or rotating contact that can be used as an adjustable potential divider. A potentiometer can be used as a rheostat or a variable resistor.
A potentiometer consists of a long resistive wire and a battery of known emf, the ends of the wire are connected to the terminals of the battery so that the potential of the battery is distributed along the wire.
The potentiometer works on the principle that the potential difference is directly proportional to the length of the wire. Therefore,
$\begin{align}
  & E\propto l \\
 & \Rightarrow E=kl \\
\end{align}$
Here, $E$ is the potential difference
$k$ is the potential per unit length
$l$ is the length of the wire
(a). The potentiometer can be used to compare the emf of two cells.
Two cells are taken and one of the cells is connected to one end of the potentiometer wire while the other end is connected to a galvanometer which in turn is connected to a slider.
The slider is then moved along the potentiometer wire. The point along the wire at which the galvanometer shows null deflection is the length that is proportional to the emf of that cell. Now, the first cell is removed and the same process is repeated for the second cell. The lengths for both the cells are recorded. The emf of both the cells is compared using the following relation,
$\dfrac{{{E}_{1}}}{{{E}_{2}}}=\dfrac{{{l}_{1}}}{{{l}_{2}}}$
Here, ${{E}_{1}},\,{{E}_{2}}$ are emfs of both cells respectively and ${{l}_{1}},\,{{l}_{2}}$ are lengths corresponding to each emf.
(b). In order to calculate the internal resistance of a cell we first calculate its emf for that, one of its terminals is connected to one end of the wire and the other terminal is connected to a galvanometer which in turn is connected to the slider. The slider is moved along the length of the potentiometer wire. The point at which the galvanometer gives null deflection is the point is the length that corresponds to its emf. Using $E=kl$ we calculate the emf.
Now, we connect the other terminal of the battery to a resistance box which is connected to the galvanometer and slider. The slider is moved along the wire and the same process is repeated. The length obtained corresponds to the potential difference, $V$.
We know that,
$E-V=Ir$
Here, $I$ is the current
$r$ is the internal resistance
Substituting obtained values in the above equation, we can calculate internal resistance.
Therefore, a potentiometer is an instrument which is used to calculate the potential difference. It works on the principle that potential is directly proportional to its length. Potentiometer can be used to compare emf of two cells or calculate internal resistance for a cell.

Note:
You can check the connections on the potentiometer by keeping the slider on different ends of the wire and checking the deflections on the galvanometer. If the needle of the galvanometer gets deflected only in one direction, the connections are wrong. Moving the slider too harshly on the wire may cause wear and tear.