The electromotive force (emf) is the potential difference of a source when no current is flowing. Terminal voltage is the voltage output of a device is measured across its terminals. Terminal voltage is calculated by V = emf - Ir

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**Terminal Potential Difference of a Battery vs Terminal Voltage of a Cell**

The terminal potential difference of a battery and the terminal voltage of a cell are related concepts that describe the electrical potential difference between the positive and negative terminals of a power source. While they are often used interchangeably, there are slight differences between the two terms.

**Terminal Potential Difference of a Battery:**

The terminal potential difference of a battery refers to the potential difference across the terminals of a battery when it is not connected to any external circuit. It is also known as the open circuit voltage. In this state, the battery is not supplying any current and there is no voltage drop across any internal resistance. The terminal potential difference represents the maximum potential difference that the battery can provide.

**Terminal Voltage of a Cell:**

The terminal voltage of a cell, on the other hand, refers to the potential difference across the terminals of a cell when it is connected to an external circuit and is supplying current. In this state, there may be voltage drops across internal resistances due to the flow of current, which can reduce the terminal voltage compared to the open circuit voltage. The terminal voltage represents the actual potential difference available to the external circuit.

In summary, the terminal potential difference of a battery is the potential difference when it is not connected to any external circuit, while the terminal voltage of a cell is the potential difference when it is connected and supplying current to an external circuit.

**Difference between EMF and Terminal Potential Difference/Voltage:**

The electromotive force (EMF) of a battery or cell is the maximum potential difference that it can provide when no current is flowing through it. It is equal to the open circuit voltage or terminal potential difference. The EMF represents the energy per unit charge provided by the source.

On the other hand, the terminal potential difference or terminal voltage is the potential difference across the terminals of a battery or cell when it is connected to an external circuit and current is flowing. It is equal to the EMF minus any voltage drops across internal resistances.

Therefore, the main difference between EMF and terminal potential difference/voltage is that EMF represents the maximum potential difference a battery or cell can provide, while the terminal potential difference/voltage represents the actual potential difference available to the external circuit taking into account any internal voltage drops.