The electromotive force (emf) of a cell is always greater than its terminal voltage due to the presence of internal resistance within the cell. Here's a detailed explanation of why this is the case:
### Definitions
1. **Emf (Electromotive Force):** The emf of a cell is the maximum potential difference between its terminals when no current is flowing through the cell. It represents the energy provided by the cell per unit charge.
2. **Terminal Voltage:** The terminal voltage is the potential difference between the terminals of the cell when current is flowing. This is the voltage you actually measure when the cell is connected to an external circuit.
### Internal Resistance and Its Effect
Cells have internal resistance, which is the resistance to the flow of current within the cell itself. This internal resistance affects the terminal voltage of the cell in the following way:
1. **Internal Resistance (r):** This is the resistance encountered by the current as it flows through the cell's internal components. It can be due to the electrolyte, electrodes, and other internal structures.
2. **Current (I):** When a current flows through the cell, it encounters the internal resistance.
### Relationship Between Emf, Terminal Voltage, and Internal Resistance
When a current \( I \) flows through a cell with internal resistance \( r \), the terminal voltage \( V_{\text{terminal}} \) can be described by the following equation:
\[ V_{\text{terminal}} = \text{emf} - I \cdot r \]
Here’s a breakdown of this equation:
- **Emf:** This is the voltage the cell would provide if no current were flowing.
- **\( I \cdot r \):** This term represents the voltage drop across the internal resistance due to the current.
### Explanation
- **Voltage Drop Across Internal Resistance:** When current flows through the internal resistance, a portion of the emf is used up in overcoming this resistance. This results in a reduction of the terminal voltage compared to the emf.
- **Terminal Voltage Less Than Emf:** Because the internal resistance causes a voltage drop as the current flows, the voltage available at the cell’s terminals (i.e., the terminal voltage) is less than the emf.
### Practical Example
Consider a simple example where a cell has an emf of 12V and an internal resistance of 1 ohm. If the cell supplies a current of 2A, the voltage drop across the internal resistance is:
\[ \text{Voltage Drop} = I \cdot r = 2 \, \text{A} \cdot 1 \, \text{ohm} = 2 \, \text{V} \]
Therefore, the terminal voltage is:
\[ V_{\text{terminal}} = \text{emf} - \text{Voltage Drop} = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V} \]
In this case, the terminal voltage is 10V, which is less than the emf of 12V due to the internal resistance.
### Summary
The emf of a cell is always greater than its terminal voltage because of the internal resistance of the cell. The internal resistance causes a voltage drop when current flows, leading to a reduction in the terminal voltage compared to the emf.