Why emf is always greater than its terminal voltage?
2 Answers
To understand why the electromotive force (emf) of a battery or cell is always greater than its terminal voltage, let’s break down the concepts and the reasoning behind this phenomenon.
### Key Concepts
1. **Electromotive Force (emf)**: This is the maximum potential difference between the terminals of a cell when no current is flowing. It represents the energy supplied by the cell per unit charge.
2. **Terminal Voltage**: This is the potential difference across the terminals of a cell when it is supplying current to an external circuit. The terminal voltage is less than the emf when the cell is in use.
3. **Internal Resistance**: This is the resistance offered by the internal components of the cell to the flow of current. It causes a drop in the voltage inside the cell when current flows.
### Relationship Between emf and Terminal Voltage
When a cell is connected to an external circuit, current flows through the circuit and also through the internal resistance of the cell. This results in a voltage drop inside the cell due to the internal resistance.
#### Formula for Terminal Voltage
The terminal voltage (\( V_{terminal} \)) of a cell can be calculated using the formula:
\[ V_{terminal} = \text{emf} - I \cdot r_{internal} \]
where:
- \(\text{emf}\) is the electromotive force of the cell,
- \(I\) is the current flowing through the circuit,
- \(r_{internal}\) is the internal resistance of the cell.
### Explanation
1. **Internal Resistance Effect**: When current flows through the cell, the internal resistance causes a voltage drop. This drop reduces the voltage available across the external terminals. The greater the current and internal resistance, the larger this voltage drop will be.
2. **No Current Condition**: When no current flows (i.e., the circuit is open), the terminal voltage equals the emf because there is no internal voltage drop. However, in a real-world scenario where current is being supplied, the internal resistance always causes a reduction in terminal voltage compared to the emf.
3. **Practical Example**: Imagine a battery with an emf of 12V and an internal resistance of 1 ohm. If the battery is supplying a current of 2A, the voltage drop due to internal resistance is \( I \cdot r_{internal} = 2 \text{ A} \times 1 \text{ ohm} = 2 \text{ V} \). Therefore, the terminal voltage is \( 12 \text{ V} - 2 \text{ V} = 10 \text{ V} \). This shows that the terminal voltage is always less than the emf when current is flowing.
### Summary
The emf of a cell is always greater than its terminal voltage when current is flowing due to the internal resistance of the cell. The internal resistance causes a voltage drop inside the cell, which reduces the potential difference across the terminals. Thus, in any practical situation where the cell is active and current is flowing, the terminal voltage will be less than the emf.
### Key Concepts
1. **Electromotive Force (emf)**: This is the maximum potential difference between the terminals of a cell when no current is flowing. It represents the energy supplied by the cell per unit charge.
2. **Terminal Voltage**: This is the potential difference across the terminals of a cell when it is supplying current to an external circuit. The terminal voltage is less than the emf when the cell is in use.
3. **Internal Resistance**: This is the resistance offered by the internal components of the cell to the flow of current. It causes a drop in the voltage inside the cell when current flows.
### Relationship Between emf and Terminal Voltage
When a cell is connected to an external circuit, current flows through the circuit and also through the internal resistance of the cell. This results in a voltage drop inside the cell due to the internal resistance.
#### Formula for Terminal Voltage
The terminal voltage (\( V_{terminal} \)) of a cell can be calculated using the formula:
\[ V_{terminal} = \text{emf} - I \cdot r_{internal} \]
where:
- \(\text{emf}\) is the electromotive force of the cell,
- \(I\) is the current flowing through the circuit,
- \(r_{internal}\) is the internal resistance of the cell.
### Explanation
1. **Internal Resistance Effect**: When current flows through the cell, the internal resistance causes a voltage drop. This drop reduces the voltage available across the external terminals. The greater the current and internal resistance, the larger this voltage drop will be.
2. **No Current Condition**: When no current flows (i.e., the circuit is open), the terminal voltage equals the emf because there is no internal voltage drop. However, in a real-world scenario where current is being supplied, the internal resistance always causes a reduction in terminal voltage compared to the emf.
3. **Practical Example**: Imagine a battery with an emf of 12V and an internal resistance of 1 ohm. If the battery is supplying a current of 2A, the voltage drop due to internal resistance is \( I \cdot r_{internal} = 2 \text{ A} \times 1 \text{ ohm} = 2 \text{ V} \). Therefore, the terminal voltage is \( 12 \text{ V} - 2 \text{ V} = 10 \text{ V} \). This shows that the terminal voltage is always less than the emf when current is flowing.
### Summary
The emf of a cell is always greater than its terminal voltage when current is flowing due to the internal resistance of the cell. The internal resistance causes a voltage drop inside the cell, which reduces the potential difference across the terminals. Thus, in any practical situation where the cell is active and current is flowing, the terminal voltage will be less than the emf.