Question

Is the emf of a battery equal to its terminal potential difference?

Answer 1

To clarify your question, are you asking about the relationship between the electromotive force (emf) of a battery and the terminal potential difference under specific conditions, such as when the battery is under load?

Answer 2

No, the electromotive force (EMF) of a battery is not necessarily equal to its terminal potential difference. Here’s why:

### EMF vs. Terminal Potential Difference

1. **Electromotive Force (EMF)**:
   - EMF is a measure of the maximum potential difference between the terminals of a battery when no current is flowing through the circuit. It's essentially the voltage provided by the battery due to chemical reactions occurring inside it.
   - EMF represents the total energy per unit charge supplied by the battery.

2. **Terminal Potential Difference**:
   - The terminal potential difference is the actual voltage across the terminals of the battery when a current is flowing through the circuit.
   - This can be different from the EMF due to the internal resistance of the battery.

### Relationship Between EMF and Terminal Potential Difference

The terminal potential difference (V) when current (I) is flowing through a circuit is given by:

\[ V = \text{EMF} - I \cdot r_{\text{internal}} \]

where:
- \(\text{EMF}\) is the electromotive force of the battery.
- \(I\) is the current flowing through the circuit.
- \(r_{\text{internal}}\) is the internal resistance of the battery.

### Key Points

- **Without Current**: When there is no current (I = 0), the terminal potential difference equals the EMF.
- **With Current**: When current flows, the terminal potential difference is less than the EMF due to the voltage drop across the internal resistance.

### Example

If a battery has an EMF of 12V and an internal resistance of 1Ω, and if it supplies a current of 2A, the terminal potential difference would be:

\[ V = \text{EMF} - I \cdot r_{\text{internal}} \]
\[ V = 12V - 2A \cdot 1Ω \]
\[ V = 12V - 2V \]
\[ V = 10V \]

So, the terminal potential difference (10V) is less than the EMF (12V) because of the internal resistance.

In summary, the EMF of a battery is the maximum potential difference when no current flows, while the terminal potential difference is what you actually measure when the battery is supplying current, which is always less than or equal to the EMF depending on the internal resistance and the current.