Potentiometer

A potentiometer is a three-terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. It is widely used in electronics to measure the electromotive force (emf) of a cell, compare emfs of different cells, and for various other purposes like volume control in audio devices.

Principle of Operation

The potentiometer works on the principle that when a constant current flows through a wire of uniform cross-sectional area and composition, the potential difference across any segment of the wire is directly proportional to the length of that segment.

Mathematically, this can be expressed as:

$$ V = I \cdot R $$

where ( V ) is the potential difference, ( I ) is the current, and ( R ) is the resistance. For a uniform wire, ( R ) is proportional to the length ( L ), so we can write:

$$ V = I \cdot (\rho \cdot \frac{L}{A}) $$

where ( \rho ) is the resistivity of the material and ( A ) is the cross-sectional area.

Construction

A potentiometer consists of a long wire of uniform cross-section wound on an insulating cylindrical core. This wire is usually made of materials like constantan or manganin due to their high resistivity and low temperature coefficients. The ends of the wire are connected to a battery with a known voltage, which provides a constant current. A sliding contact, known as the jockey, can move along the wire to tap off a voltage at any point.

Types of Potentiometers

There are mainly two types of potentiometers:

Rotary Potentiometer: It has a circular resistive element and a rotating wiper contact.
Linear Potentiometer: It has a straight resistive element and a sliding wiper contact.

Applications

Measuring Voltage: It can measure unknown voltages by comparing them with a known voltage.
Measuring Internal Resistance of a Cell: It can be used to find the internal resistance of a cell by comparing potential drops.
Calibrating Instruments: It can calibrate voltmeters and ammeters.
Control Applications: It is used as a control device for volume, light intensity, and motion control.

Potentiometer vs Voltmeter

Here's a comparison between a potentiometer and a voltmeter:

Feature	Potentiometer	Voltmeter
Principle	Works on the principle of a null method where no current flows through the circuit when measuring potential difference.	Works on the principle of deflection where the needle moves in response to current flowing through the circuit.
Accuracy	More accurate as it does not draw current from the circuit being measured.	Less accurate as it draws current and can alter the circuit conditions.
Sensitivity	High sensitivity due to the null method.	Lower sensitivity compared to a potentiometer.
Usage	Used for precise measurements.	Used for quick and less precise measurements.
Complexity	More complex setup with a jockey and a long wire.	Simple device with a dial and needle.

Formulas and Examples

Voltage Measurement

To measure the voltage of a cell using a potentiometer, we use the formula:

$$ V_x = \frac{L_x}{L} \cdot V $$

where:

( V_x ) is the unknown voltage of the cell.
( L_x ) is the length of the wire from the starting point to the point where the null deflection occurs.
( L ) is the total length of the potentiometer wire.
( V ) is the known voltage supplied to the potentiometer wire.

Example: If a potentiometer wire of 10 meters is supplied with 2 volts and the null deflection occurs at 4 meters, the voltage of the cell is:

$$ V_x = \frac{4 \text{ meters}}{10 \text{ meters}} \cdot 2 \text{ volts} = 0.8 \text{ volts} $$

Internal Resistance of a Cell

The internal resistance ( r ) of a cell can be calculated using the potentiometer by first measuring the terminal voltage ( V_T ) of the cell when no current is drawn from it (open-circuit condition) and then measuring the terminal voltage ( V_L ) when a known resistance ( R ) is connected across the cell. The formula used is:

$$ r = R \left( \frac{V_T}{V_L} - 1 \right) $$

Example: If the open-circuit voltage ( V_T ) is 1.5 volts and the loaded voltage ( V_L ) is 1.2 volts with a known resistance of 10 ohms, the internal resistance of the cell is:

$$ r = 10 \left( \frac{1.5}{1.2} - 1 \right) = 2.5 \text{ ohms} $$

In conclusion, the potentiometer is a versatile instrument used in various applications requiring precise and accurate measurements. Its ability to measure without drawing current from the circuit makes it a valuable tool in electrical and electronic measurements.