Question

A Leclanche cell gets balanced on the wire of a potentiometer at 280 cm. If a Daniel cell is joined in series with a Leclanche cell, then the balance point is obtained at 480 cm. Compare the e.m.f. of two cells.

Answer 1

Hint: The potentiometer sensitivity is the smallest voltage difference. It is measured with the help of a potentiometer. The potentiometer sensitivity can increase by increasing the length of the resistance per unit voltage. Here, you need to use the condition of comparison of emf in the potentiometer and then substitute the values accordingly to solve the question.

Complete step by step answer:
According to the question:
\[{E_1} = \rho l1\]
$\implies$ \[{E_1} + {E_2} = \rho {l_2}\]
We know that, for Comparison of emf in Potentiometer we have
\[\dfrac{{{E_1}}}{{{E_2}}} = \dfrac{{{l_1}}}{{{l_2}}}\]
Now, we have
\[\dfrac{{{E_1} + {E_2}}}{{{E_1}}} = \dfrac{{\rho {l_2}}}{{\rho {l_1}}} = \dfrac{{{l_2}}}{{{l_1}}}\]
$\implies$ \[1 + \dfrac{{{E_2}}}{{{E_1}}} = \dfrac{{{l_2}}}{{{l_1}}}\]
$\implies$ \[\dfrac{{{E_2}}}{{{E_1}}} = \dfrac{{{l_2}}}{{{l_1}}} - 1 = \dfrac{{{l_2} - {l_1}}}{{{l_1}}}\]
$\implies$ \[\dfrac{{{E_1}}}{{{E_2}}} = \dfrac{{{l_1}}}{{{l_2} - {l_1}}} = \dfrac{{280}}{{480 - 280}} = \dfrac{{280}}{{200}}\]
\[{E_1}:{E_2} = 7:5\]

Following are the uses of a potentiometer. The three major applications of a potentiometer are:
- Comparing the emf of a battery cell with a standard cell.
- Measuring the internal resistance of a battery cell.
- Measuring the voltage across a branch of a circuit.

There are various advantages of the Potentiometer. Here is some listed advantages of Potentiometer:
- It offers higher reliability.
- It has Increased accuracy.
- Small in size, multiple potentiometers can be packed on a single chip.
- Negligible resistance drift.
- It can’t be affected by different environmental conditions such as vibrations, humidity, shocks and wiper contamination etc.

Note:
There are two main types of potentiometers:
1. Rotary potentiometer
2. Linear potentiometer
Both of the potentiometers have different constructional features but the working principle of both types of potentiometers is very similar to another.