What is the relationship between emf and terminal potential?
2 Answers
The electromotive force (emf) and the terminal potential difference of a battery or power source are related concepts but distinct in their meanings.
1. **Electromotive Force (emf)**: This is the maximum potential difference generated by a battery or power source when no current is flowing. It represents the energy provided per unit charge by the source. Emf is a measure of the ability of the source to do work on charges.
2. **Terminal Potential Difference**: This is the actual voltage measured across the terminals of the battery when it is connected to a circuit and current is flowing. It can be less than the emf due to internal resistance within the battery.
### Relationship:
- When no current flows (open circuit), the terminal potential difference equals the emf.
- When a load is connected and current flows, the terminal potential is less than the emf due to the voltage drop caused by the internal resistance of the battery, described by the equation:
\[
V = \text{emf} - I \cdot r
\]
where \( V \) is the terminal potential difference, \( I \) is the current, and \( r \) is the internal resistance of the battery.
In summary, the emf is the ideal voltage output under no-load conditions, while the terminal potential difference accounts for the effects of internal resistance when a load is applied.
1. **Electromotive Force (emf)**: This is the maximum potential difference generated by a battery or power source when no current is flowing. It represents the energy provided per unit charge by the source. Emf is a measure of the ability of the source to do work on charges.
2. **Terminal Potential Difference**: This is the actual voltage measured across the terminals of the battery when it is connected to a circuit and current is flowing. It can be less than the emf due to internal resistance within the battery.
### Relationship:
- When no current flows (open circuit), the terminal potential difference equals the emf.
- When a load is connected and current flows, the terminal potential is less than the emf due to the voltage drop caused by the internal resistance of the battery, described by the equation:
\[
V = \text{emf} - I \cdot r
\]
where \( V \) is the terminal potential difference, \( I \) is the current, and \( r \) is the internal resistance of the battery.
In summary, the emf is the ideal voltage output under no-load conditions, while the terminal potential difference accounts for the effects of internal resistance when a load is applied.
The relationship between electromotive force (emf) and terminal potential (or terminal voltage) is a key concept in understanding how electrical circuits work. Here's a detailed explanation:
### Electromotive Force (emf)
- **Definition**: Electromotive force (emf) is the total energy supplied by a source per coulomb of charge that passes through it. It represents the maximum potential difference that a power source (like a battery or generator) can provide when no current is flowing.
- **Symbol**: ε (epsilon)
- **Nature**: It is an ideal concept that assumes no internal resistance in the source.
### Terminal Potential (Terminal Voltage)
- **Definition**: Terminal potential, or terminal voltage, is the actual voltage available across the terminals of a power source when it is connected to a circuit and current is flowing.
- **Symbol**: V (or sometimes \( V_{\text{term}} \))
- **Nature**: It is the effective voltage that is available to the external circuit after accounting for any internal resistance of the power source.
### Relationship Between emf and Terminal Potential
The relationship between emf and terminal potential can be described by the following formula:
\[ V = \epsilon - I \cdot r \]
where:
- \( V \) = Terminal potential (voltage across the terminals)
- \( \epsilon \) = Electromotive force (emf) of the source
- \( I \) = Current flowing through the circuit
- \( r \) = Internal resistance of the source
### Key Points:
1. **No Current Flow**: When no current is flowing (i.e., in an open circuit), the terminal potential equals the emf of the source. This is because the internal resistance does not affect the voltage when there is no current.
2. **With Current Flow**: When current flows through the circuit, the internal resistance of the power source causes a voltage drop inside the source. This voltage drop is given by \( I \cdot r \). Thus, the terminal potential is less than the emf by this amount.
3. **Internal Resistance Effect**: The internal resistance of the source causes the terminal potential to decrease from the emf value as current increases. For larger currents, the voltage drop due to internal resistance becomes more significant, leading to a greater difference between emf and terminal potential.
4. **Practical Example**: In a real battery, if the emf is 12 volts and the internal resistance is 1 ohm, then if a current of 2 amps is flowing, the terminal potential would be:
\[
V = \epsilon - I \cdot r = 12\,\text{V} - 2\,\text{A} \times 1\,\text{Ω} = 10\,\text{V}
\]
Thus, the terminal voltage available to the external circuit is 10 volts.
Understanding this relationship is crucial for analyzing and designing electrical circuits, as it affects how much voltage is actually available for use in various components and devices connected to the circuit.
### Electromotive Force (emf)
- **Definition**: Electromotive force (emf) is the total energy supplied by a source per coulomb of charge that passes through it. It represents the maximum potential difference that a power source (like a battery or generator) can provide when no current is flowing.
- **Symbol**: ε (epsilon)
- **Nature**: It is an ideal concept that assumes no internal resistance in the source.
### Terminal Potential (Terminal Voltage)
- **Definition**: Terminal potential, or terminal voltage, is the actual voltage available across the terminals of a power source when it is connected to a circuit and current is flowing.
- **Symbol**: V (or sometimes \( V_{\text{term}} \))
- **Nature**: It is the effective voltage that is available to the external circuit after accounting for any internal resistance of the power source.
### Relationship Between emf and Terminal Potential
The relationship between emf and terminal potential can be described by the following formula:
\[ V = \epsilon - I \cdot r \]
where:
- \( V \) = Terminal potential (voltage across the terminals)
- \( \epsilon \) = Electromotive force (emf) of the source
- \( I \) = Current flowing through the circuit
- \( r \) = Internal resistance of the source
### Key Points:
1. **No Current Flow**: When no current is flowing (i.e., in an open circuit), the terminal potential equals the emf of the source. This is because the internal resistance does not affect the voltage when there is no current.
2. **With Current Flow**: When current flows through the circuit, the internal resistance of the power source causes a voltage drop inside the source. This voltage drop is given by \( I \cdot r \). Thus, the terminal potential is less than the emf by this amount.
3. **Internal Resistance Effect**: The internal resistance of the source causes the terminal potential to decrease from the emf value as current increases. For larger currents, the voltage drop due to internal resistance becomes more significant, leading to a greater difference between emf and terminal potential.
4. **Practical Example**: In a real battery, if the emf is 12 volts and the internal resistance is 1 ohm, then if a current of 2 amps is flowing, the terminal potential would be:
\[
V = \epsilon - I \cdot r = 12\,\text{V} - 2\,\text{A} \times 1\,\text{Ω} = 10\,\text{V}
\]
Thus, the terminal voltage available to the external circuit is 10 volts.
Understanding this relationship is crucial for analyzing and designing electrical circuits, as it affects how much voltage is actually available for use in various components and devices connected to the circuit.