**Difference Between EMF and Terminal Potential Difference of a Battery**

The electromotive force (EMF) and terminal potential difference of a battery are two important concepts in the study of electrical circuits. While they are related, they represent different aspects of a battery's behavior. Let's explore the difference between EMF and terminal potential difference in detail.

**Electromotive Force (EMF)**

- **Definition**: The electromotive force (EMF) of a battery is the maximum potential difference that the battery can provide when no current is flowing through it.
- **Source**: EMF is the voltage produced by the chemical reactions inside the battery that convert chemical energy into electrical energy.
- **Internal Resistance**: Every battery has some internal resistance due to the materials used in its construction. When a current flows through the battery, this internal resistance causes a voltage drop, reducing the terminal potential difference.
- **Ideal Battery**: In an ideal battery, the internal resistance is considered to be zero, resulting in the terminal potential difference being equal to the EMF. However, in practical batteries, there is always some internal resistance present.
- **Unit**: EMF is measured in volts (V).

**Terminal Potential Difference**

- **Definition**: The terminal potential difference is the actual potential difference across the terminals of a battery when current is flowing through it.
- **Voltage Drop**: When a current flows through a battery, the internal resistance causes a voltage drop. This voltage drop reduces the terminal potential difference from the EMF.
- **Measuring**: The terminal potential difference can be measured using a voltmeter connected across the terminals of the battery while it is in a circuit.
- **Unit**: Terminal potential difference is also measured in volts (V).

**Relation between EMF and Terminal Potential Difference**

The terminal potential difference (V) of a battery is related to its electromotive force (E) and internal resistance (r) through Ohm's law:

V = E - Ir

where V is the terminal potential difference, E is the EMF, and I is the current flowing through the battery.

**Conclusion**

In summary, the electromotive force (EMF) of a battery represents the maximum potential difference it can provide when no current is flowing. On the other hand, the terminal potential difference is the actual potential difference across the battery's terminals when current is flowing. The terminal potential difference is reduced from the EMF due to the presence of internal resistance in the battery. Understanding the difference between EMF and terminal potential difference is crucial for analyzing and designing electrical circuits.

Emf is the potential difference across the terminals of a cell when it is not delivering any current while terminal potential difference is the potential difference across it's terminal when current is drawn through a cell or current is supplied to it.