Potentiometer in Physics: Definition, Principle, Working and Uses

A potentiometer is an electrical instrument used to measure or compare the electromotive force (EMF) of cells and to measure potential differences accurately. It works by balancing an unknown voltage against the potential drop along a uniform resistance wire.

1. Principle of a Potentiometer

The principle of a potentiometer states that when a constant current flows through a uniform wire of uniform cross-sectional area, the potential drop across any part of the wire is directly proportional to its length.

This means that if the length of the wire is doubled while the current remains constant, the potential drop across that length also doubles.

Therefore, we can write:

Here:

• V = potential drop across the wire segment
• L = length of the wire segment
• k = potential gradient, or potential drop per unit length

The potential gradient is expressed in volts per metre (V/m) or volts per centimetre (V/cm), depending on the unit used for length.

2. Construction of a Potentiometer

A typical laboratory potentiometer consists of the following parts:

• Uniform resistance wire: A long wire of uniform material and cross-sectional area along which a potential gradient is established.
• Driving battery: Supplies current through the potentiometer wire.
• Rheostat: Adjusts the current in the primary circuit.
• Galvanometer: Detects whether current flows through the measuring branch.
• Jockey: A movable contact used to touch different points on the wire.
• Cell under test: The cell whose EMF or potential difference is to be measured.

3. Working of a Potentiometer

A potentiometer works by comparing the unknown voltage with the voltage developed along a known length of wire. Its operation can be understood in these steps:

1. A steady current is passed through the uniform potentiometer wire using the driving battery.
2. The cell under test is connected to the measuring circuit through a galvanometer and jockey.
3. The jockey is moved along the wire to find a position where the galvanometer shows zero deflection.
4. At this position, the potential drop along the selected wire length balances the EMF of the cell, provided the cell supplies no current through the measuring branch.
5. The balancing length is measured and used to calculate the unknown voltage.

4. What Is the Null Point?

The null point, also called the balance point, is the position on the potentiometer wire at which the potential drop along the wire equals the EMF being measured.

At this point, the galvanometer shows zero deflection because there is no potential difference driving current through the measuring branch. This is the key to accurate potentiometer measurements.

5. Potential Gradient of a Potentiometer

The potential gradient is the potential drop per unit length of the potentiometer wire. It is represented by the letter k.

If a potential difference of 2 V is established across a 4 m long uniform wire, the potential gradient is:

6. Comparing the EMFs of Two Cells

A potentiometer can compare the EMFs of two cells by finding their respective balancing lengths while keeping the current in the potentiometer wire unchanged.

Let:

• E₁ and E₂ be the EMFs of the two cells.
• L₁ and L₂ be their respective balancing lengths.
• k be the same potential gradient for both measurements.

For the first cell:

For the second cell:

Dividing the two equations gives:

Thus, the ratio of the EMFs equals the ratio of their balancing lengths, provided both measurements use the same potential gradient.

7. Why Is a Potentiometer More Accurate Than a Voltmeter?

An ordinary voltmeter draws a small current from the circuit because it has finite resistance. This can slightly change the voltage being measured.

A potentiometer uses a null method. At the balance point, an ideal potentiometer draws no current from the cell under test through the measuring branch. Therefore, the cell's EMF can be measured without the loading error caused by that measuring current.

Its accuracy still depends on factors such as the uniformity of the wire, stability of the current, contact quality and the sensitivity of the galvanometer.

8. Uses of a Potentiometer

• Measuring EMF: To determine the EMF of a cell using a suitable balance circuit.
• Comparing cell EMFs: To compare the EMFs of two cells using their balancing lengths.
• Measuring potential difference: To measure a potential difference by balancing it against the potential drop along the wire.
• Finding internal resistance: To determine the internal resistance of a cell using appropriate circuit connections and measurements.
• Physics experiments: To demonstrate potential drop, potential gradient and the null method in electrical circuits.

9. Potentiometer vs Voltmeter

10. Important Points for Exams

• The potentiometer works on the principle V ∝ L.
• The current through the uniform wire must remain constant for the potential gradient to remain constant.
• The null point is the point of zero galvanometer deflection.
• At balance, the potential drop along the wire equals the voltage being measured.
• For two cells, E₁/E₂ = L₁/L₂ when the same potential gradient is used.
• A longer balancing length corresponds to a greater EMF under the same conditions.

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