Question

Is the terminal potential difference of a cell equal to emf?

Answer 1

Not exactly. The terminal potential difference of a cell can be less than its EMF due to internal resistance and load conditions. Would you like to delve deeper into how these factors affect the measurements?

Answer 2

The terminal potential difference of a cell is not always equal to its electromotive force (EMF). Understanding the difference between these two concepts requires a look at how they are defined and the factors affecting them.

### Definitions

1. **Electromotive Force (EMF)**: EMF is a measure of the energy provided by a cell or battery per coulomb of charge as it moves through the cell. It represents the maximum potential difference the cell can provide when no current is flowing. In essence, EMF is the "ideal" voltage of the cell when it is not connected to any external circuit.

2. **Terminal Potential Difference**: This is the voltage measured across the terminals of the cell when it is connected to an external circuit and current is flowing. It is the actual voltage available to the external circuit.

### Relationship Between EMF and Terminal Potential Difference

The terminal potential difference \( V_{terminal} \) of a cell is given by:

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

where:
- \( I \) is the current flowing through the circuit.
- \( r_{internal} \) is the internal resistance of the cell.

### Key Points

- **Internal Resistance**: Every real cell has some internal resistance, which is the resistance to the flow of current within the cell itself. When a current \( I \) flows through the cell, there is a voltage drop across this internal resistance, which is \( I \cdot r_{internal} \). This reduces the terminal potential difference compared to the EMF.

- **No Current Flow**: When no current is flowing (i.e., when the cell is not connected to any external load), the terminal potential difference is equal to the EMF of the cell. This is because there is no voltage drop across the internal resistance if no current is present.

- **Under Load**: When a cell is connected to an external circuit and current flows, the terminal potential difference will be less than the EMF due to the voltage drop caused by the internal resistance.

### Example

Suppose a cell has an EMF of 12 V and an internal resistance of 1 Ω. If the cell is connected to a circuit with a load resistance of 11 Ω, the total resistance in the circuit is 12 Ω. If a current \( I \) of 1 A flows through the circuit, the voltage drop across the internal resistance is \( 1 \, \text{A} \times 1 \, \text{Ω} = 1 \, \text{V} \).

So, the terminal potential difference is:

\[ V_{terminal} = 12 \, \text{V} - 1 \, \text{V} = 11 \, \text{V} \]

This shows how the terminal potential difference can be less than the EMF when there is a current flowing through the cell.