Consider a potentiometer set-up where a cell of emf 2.25 V gives a balance point at 63.0 cm length of the wire. Now the cell is replaced by another cell and the balance point shifts to 21.0 cm. Then the emf of the second cell is:

Concept:

Potentiometer:

• The potentiometer is basically a long piece of uniform wire across which a standard cell is connected.
• The basic principle of the potentiometer is that the potential drop across any section of the wire will be directly proportional to the length of the wire, provided the wire is of a uniform cross-sectional area and a uniform current flows through the wire.

• The relation gives the balanced condition, E₁ l₂ = E₂ l₁
• The potentiometer is an instrument used for measuring the unknown voltage by comparing it with the known voltage.
• It can be used to determine the emf and internal resistance of the given cell and to compare the emf of different cells.
• The comparative method is used by the potentiometer.
• The reading is more accurate in a potentiometer.

Calculation:

Given,

The emf of the cell, E₁ = 2.25 V

The balance point of the potentiometer, l₁ = 63.0 cm

Now, the cell is replaced by another cell with emf, E₂ = ?

The balance point, l₂ = 21.0 cm

The relation gives the balanced condition,

\(\frac{E_1}{E_2}=\frac{l_1}{l_2}\)

\(\Rightarrow E_2=\frac{E_1\times l_2}{l_1}\)

\(\Rightarrow E_2=\frac{2.25\times 21}{63} = 0.75~V\)

Hence, the emf of the second cell is 0.75V.