What is the difference between terminal potential difference and emf?
2 Answers
The **terminal potential difference** and the **electromotive force (emf)** are two important concepts in electrical circuits, and they are closely related, but not the same. Here's a detailed explanation of their differences:
### 1. **Electromotive Force (emf)**:
- **Definition**: EMF is the total energy provided by a source, such as a battery or generator, to move one coulomb of charge around a complete circuit. It is the energy per unit charge supplied by the chemical reaction or mechanical work inside the source.
- **Ideal Condition**: EMF represents the maximum potential difference across the terminals of a source when **no current is flowing**, i.e., in an open circuit.
- **Unit**: Volts (V).
- **Representation**: It is typically represented by the symbol **ε**.
- **Cause**: It is due to the internal energy sources (chemical, mechanical, etc.) inside the cell or generator that drive the movement of charges.
For example, a 12 V battery has an emf of 12 volts, meaning it supplies 12 joules of energy for every coulomb of charge.
### 2. **Terminal Potential Difference**:
- **Definition**: The terminal potential difference is the actual voltage across the terminals of a source (like a battery) **when current is flowing** through the circuit.
- **Effect of Internal Resistance**: The terminal potential difference is usually **less than** the emf when the current flows through the circuit due to the **internal resistance** of the source. This internal resistance causes a voltage drop inside the battery or generator.
- **Unit**: Volts (V).
- **Relation to Current**: When a current is flowing, the terminal potential difference decreases because of the internal resistance, which leads to a voltage drop given by \( V = \varepsilon - Ir \), where:
- \( I \) = current
- \( r \) = internal resistance
If a battery has internal resistance \( r \) and delivers current \( I \), the terminal potential difference \( V \) can be calculated as:
\[ V = \varepsilon - Ir \]
### Key Differences:
1. **In Open Circuit (No Load)**:
- EMF and terminal potential difference are equal since no current flows, and there is no internal voltage drop.
2. **In Closed Circuit (Load Connected)**:
- The terminal potential difference is **less than** the emf because of the voltage drop across the internal resistance of the source.
3. **Internal Resistance Factor**:
- EMF is the theoretical voltage when no current flows, and internal resistance has no effect.
- Terminal potential difference accounts for internal resistance, reducing the voltage available to the external circuit when current is flowing.
### Summary:
- **EMF**: The maximum voltage a source can provide (open circuit, no current).
- **Terminal Potential Difference**: The actual voltage measured across the source terminals when a current flows (closed circuit, with internal resistance).
### 1. **Electromotive Force (emf)**:
- **Definition**: EMF is the total energy provided by a source, such as a battery or generator, to move one coulomb of charge around a complete circuit. It is the energy per unit charge supplied by the chemical reaction or mechanical work inside the source.
- **Ideal Condition**: EMF represents the maximum potential difference across the terminals of a source when **no current is flowing**, i.e., in an open circuit.
- **Unit**: Volts (V).
- **Representation**: It is typically represented by the symbol **ε**.
- **Cause**: It is due to the internal energy sources (chemical, mechanical, etc.) inside the cell or generator that drive the movement of charges.
For example, a 12 V battery has an emf of 12 volts, meaning it supplies 12 joules of energy for every coulomb of charge.
### 2. **Terminal Potential Difference**:
- **Definition**: The terminal potential difference is the actual voltage across the terminals of a source (like a battery) **when current is flowing** through the circuit.
- **Effect of Internal Resistance**: The terminal potential difference is usually **less than** the emf when the current flows through the circuit due to the **internal resistance** of the source. This internal resistance causes a voltage drop inside the battery or generator.
- **Unit**: Volts (V).
- **Relation to Current**: When a current is flowing, the terminal potential difference decreases because of the internal resistance, which leads to a voltage drop given by \( V = \varepsilon - Ir \), where:
- \( I \) = current
- \( r \) = internal resistance
If a battery has internal resistance \( r \) and delivers current \( I \), the terminal potential difference \( V \) can be calculated as:
\[ V = \varepsilon - Ir \]
### Key Differences:
1. **In Open Circuit (No Load)**:
- EMF and terminal potential difference are equal since no current flows, and there is no internal voltage drop.
2. **In Closed Circuit (Load Connected)**:
- The terminal potential difference is **less than** the emf because of the voltage drop across the internal resistance of the source.
3. **Internal Resistance Factor**:
- EMF is the theoretical voltage when no current flows, and internal resistance has no effect.
- Terminal potential difference accounts for internal resistance, reducing the voltage available to the external circuit when current is flowing.
### Summary:
- **EMF**: The maximum voltage a source can provide (open circuit, no current).
- **Terminal Potential Difference**: The actual voltage measured across the source terminals when a current flows (closed circuit, with internal resistance).
The terms "terminal potential difference" and "electromotive force" (emf) are both related to electrical circuits, but they represent different concepts:
### 1. **Electromotive Force (emf)**
- **Definition**: Electromotive force (emf) is the maximum potential difference between the terminals of a source (like a battery or generator) when no current is flowing. It represents the energy provided per unit charge by the source.
- **Origin**: It is generated due to chemical reactions in batteries or mechanical movement in generators.
- **Measurement**: Measured in volts (V).
- **Expression**: In an ideal scenario with no internal resistance, the emf is equal to the terminal potential difference. It is often denoted by the symbol \( \mathcal{E} \).
### 2. **Terminal Potential Difference**
- **Definition**: Terminal potential difference is the actual voltage measured across the terminals of a source when current is flowing through the circuit. It represents the actual potential difference available to drive current through an external circuit.
- **Effect of Internal Resistance**: This value is always less than the emf of the source due to the internal resistance of the source. The voltage drop inside the source (due to internal resistance) reduces the terminal potential difference.
- **Measurement**: Also measured in volts (V).
- **Expression**: Terminal potential difference (\( V \)) can be calculated using the formula:
\[
V = \mathcal{E} - I \cdot r
\]
where \( I \) is the current flowing through the circuit and \( r \) is the internal resistance of the source.
### Summary
- **emf**: The ideal, maximum potential difference of a source when no current flows. It is the source's capability to provide energy.
- **Terminal Potential Difference**: The actual voltage available across the terminals of the source when current flows, taking into account the internal resistance.
The key difference is that emf is the potential difference without current flow, while the terminal potential difference is the potential difference with current flow, which is always less due to the internal resistance.
### 1. **Electromotive Force (emf)**
- **Definition**: Electromotive force (emf) is the maximum potential difference between the terminals of a source (like a battery or generator) when no current is flowing. It represents the energy provided per unit charge by the source.
- **Origin**: It is generated due to chemical reactions in batteries or mechanical movement in generators.
- **Measurement**: Measured in volts (V).
- **Expression**: In an ideal scenario with no internal resistance, the emf is equal to the terminal potential difference. It is often denoted by the symbol \( \mathcal{E} \).
### 2. **Terminal Potential Difference**
- **Definition**: Terminal potential difference is the actual voltage measured across the terminals of a source when current is flowing through the circuit. It represents the actual potential difference available to drive current through an external circuit.
- **Effect of Internal Resistance**: This value is always less than the emf of the source due to the internal resistance of the source. The voltage drop inside the source (due to internal resistance) reduces the terminal potential difference.
- **Measurement**: Also measured in volts (V).
- **Expression**: Terminal potential difference (\( V \)) can be calculated using the formula:
\[
V = \mathcal{E} - I \cdot r
\]
where \( I \) is the current flowing through the circuit and \( r \) is the internal resistance of the source.
### Summary
- **emf**: The ideal, maximum potential difference of a source when no current flows. It is the source's capability to provide energy.
- **Terminal Potential Difference**: The actual voltage available across the terminals of the source when current flows, taking into account the internal resistance.
The key difference is that emf is the potential difference without current flow, while the terminal potential difference is the potential difference with current flow, which is always less due to the internal resistance.