What is the relationship between electric potential and emf?
2 Answers
Electric potential and electromotive force (emf) are related concepts in the study of electricity, but they describe different aspects of electric circuits.
### Electric Potential
**Electric potential** refers to the electric potential energy per unit charge at a specific point in space due to the presence of electric fields. It is a measure of the work needed to move a unit positive charge from a reference point (usually infinity) to a particular point in the electric field. The electric potential at a point is given by:
\[ V = \frac{U}{q} \]
where:
- \( V \) is the electric potential,
- \( U \) is the electric potential energy,
- \( q \) is the charge.
Electric potential is measured in volts (V), where 1 volt = 1 joule per coulomb (J/C).
### Electromotive Force (emf)
**Electromotive force (emf)** is a measure of the energy provided by a source like a battery or generator per unit charge as it moves through the external circuit. It represents the work done by the source to move charges from the negative terminal to the positive terminal within the source itself. The emf is not actually a force but a potential difference provided by the source.
For a battery or generator, the emf (\(\mathcal{E}\)) is defined as:
\[ \mathcal{E} = \frac{W}{q} \]
where:
- \( \mathcal{E} \) is the emf,
- \( W \) is the work done by the source,
- \( q \) is the charge.
### Relationship Between Electric Potential and Emf
1. **Potential Difference and emf**: The emf of a source is directly related to the potential difference between its terminals. In an ideal situation (where internal resistance is zero), the emf is equal to the potential difference across the terminals of the source when no current flows through the circuit. When the circuit is closed and current flows, the potential difference across the terminals will be less than the emf due to the internal resistance of the source.
2. **Internal Resistance Effect**: In a real source with internal resistance \(r\), the relationship between the emf (\(\mathcal{E}\)), terminal potential difference (\(V_{\text{terminal}}\)), and current (\(I\)) is given by:
\[ V_{\text{terminal}} = \mathcal{E} - I \cdot r \]
Here, \(V_{\text{terminal}}\) is the voltage across the terminals of the source when current \(I\) is flowing. The term \(I \cdot r\) represents the voltage drop due to the internal resistance of the source.
### Summary
- **Electric potential** is the potential energy per unit charge at a point in an electric field.
- **Electromotive force (emf)** is the energy per unit charge provided by a source to move charges through the circuit.
In essence, the emf of a source can be thought of as the "ideal" or maximum potential difference it can provide, while the electric potential is a more general term that describes the potential energy per charge at a specific location in the field.
### Electric Potential
**Electric potential** refers to the electric potential energy per unit charge at a specific point in space due to the presence of electric fields. It is a measure of the work needed to move a unit positive charge from a reference point (usually infinity) to a particular point in the electric field. The electric potential at a point is given by:
\[ V = \frac{U}{q} \]
where:
- \( V \) is the electric potential,
- \( U \) is the electric potential energy,
- \( q \) is the charge.
Electric potential is measured in volts (V), where 1 volt = 1 joule per coulomb (J/C).
### Electromotive Force (emf)
**Electromotive force (emf)** is a measure of the energy provided by a source like a battery or generator per unit charge as it moves through the external circuit. It represents the work done by the source to move charges from the negative terminal to the positive terminal within the source itself. The emf is not actually a force but a potential difference provided by the source.
For a battery or generator, the emf (\(\mathcal{E}\)) is defined as:
\[ \mathcal{E} = \frac{W}{q} \]
where:
- \( \mathcal{E} \) is the emf,
- \( W \) is the work done by the source,
- \( q \) is the charge.
### Relationship Between Electric Potential and Emf
1. **Potential Difference and emf**: The emf of a source is directly related to the potential difference between its terminals. In an ideal situation (where internal resistance is zero), the emf is equal to the potential difference across the terminals of the source when no current flows through the circuit. When the circuit is closed and current flows, the potential difference across the terminals will be less than the emf due to the internal resistance of the source.
2. **Internal Resistance Effect**: In a real source with internal resistance \(r\), the relationship between the emf (\(\mathcal{E}\)), terminal potential difference (\(V_{\text{terminal}}\)), and current (\(I\)) is given by:
\[ V_{\text{terminal}} = \mathcal{E} - I \cdot r \]
Here, \(V_{\text{terminal}}\) is the voltage across the terminals of the source when current \(I\) is flowing. The term \(I \cdot r\) represents the voltage drop due to the internal resistance of the source.
### Summary
- **Electric potential** is the potential energy per unit charge at a point in an electric field.
- **Electromotive force (emf)** is the energy per unit charge provided by a source to move charges through the circuit.
In essence, the emf of a source can be thought of as the "ideal" or maximum potential difference it can provide, while the electric potential is a more general term that describes the potential energy per charge at a specific location in the field.
The relationship between electric potential and electromotive force (EMF) is closely related, but they represent different physical concepts in electricity.
1. **Electric Potential**:
- Electric potential at a point is the amount of electric potential energy per unit charge at that point.
- It is a scalar quantity and is measured in volts (V).
- The difference in electric potential between two points in a circuit is called the **potential difference** or **voltage**.
2. **Electromotive Force (EMF)**:
- EMF refers to the energy provided by a source (like a battery or generator) to move charge around a complete circuit.
- It is the work done to move a unit charge through the entire circuit, including the source itself, and is also measured in volts (V).
- EMF represents the driving force that pushes charges to flow, creating a current in the circuit.
### Key Differences and Relationship:
- **EMF** is often considered the cause, while **electric potential difference** is the effect.
- **EMF** is the maximum potential difference provided by a source when no current flows, while the **potential difference** across components (like resistors) in the circuit depends on the current flowing through them.
- In real circuits, due to internal resistance in sources, the actual potential difference across the terminals of a source (terminal voltage) is usually less than the EMF when current is flowing.
In summary, EMF is the total energy supplied per charge by the source, while electric potential is the energy per charge at any point in the circuit.
1. **Electric Potential**:
- Electric potential at a point is the amount of electric potential energy per unit charge at that point.
- It is a scalar quantity and is measured in volts (V).
- The difference in electric potential between two points in a circuit is called the **potential difference** or **voltage**.
2. **Electromotive Force (EMF)**:
- EMF refers to the energy provided by a source (like a battery or generator) to move charge around a complete circuit.
- It is the work done to move a unit charge through the entire circuit, including the source itself, and is also measured in volts (V).
- EMF represents the driving force that pushes charges to flow, creating a current in the circuit.
### Key Differences and Relationship:
- **EMF** is often considered the cause, while **electric potential difference** is the effect.
- **EMF** is the maximum potential difference provided by a source when no current flows, while the **potential difference** across components (like resistors) in the circuit depends on the current flowing through them.
- In real circuits, due to internal resistance in sources, the actual potential difference across the terminals of a source (terminal voltage) is usually less than the EMF when current is flowing.
In summary, EMF is the total energy supplied per charge by the source, while electric potential is the energy per charge at any point in the circuit.