Why is electromotive force greater than potential difference?
2 Answers
To understand why electromotive force (EMF) can be greater than the potential difference in a circuit, it's essential to first grasp the definitions and distinctions between these terms:
### **Definitions**
1. **Electromotive Force (EMF):**
- **Definition:** EMF is a measure of the energy provided by a source of electrical energy, such as a battery or generator, per unit charge. It represents the maximum potential difference between the terminals of the source when no current is flowing.
- **Source of Energy:** EMF is generated by converting different forms of energy (chemical, mechanical, etc.) into electrical energy.
2. **Potential Difference (PD):**
- **Definition:** PD, also known as voltage, is the actual voltage across a component or between two points in a circuit when current is flowing. It is the work done per unit charge to move a charge from one point to another in the circuit.
- **Dependence on Circuit:** PD varies depending on the circuit components and their resistance.
### **Comparison and Explanation**
1. **Ideal vs. Real Conditions:**
- **Ideal Case (No Current):** In an ideal case where no current flows, the potential difference across the terminals of a source equals its EMF. For example, in a disconnected battery, the voltage you measure is the EMF.
- **Real Case (With Current):** When the circuit is closed and current flows, the potential difference across the terminals of the source can be less than the EMF. This reduction is due to the internal resistance of the source.
2. **Internal Resistance:**
- **Internal Resistance (r):** Real sources like batteries have an internal resistance. This resistance causes a voltage drop within the source when current flows. The EMF is the voltage that the source would provide if it had no internal resistance, while the potential difference is reduced by the voltage drop across the internal resistance.
- **Voltage Drop (I × r):** The voltage drop across the internal resistance can be calculated as \( I \times r \), where \( I \) is the current and \( r \) is the internal resistance.
3. **Relationship Between EMF and PD:**
- **Equation:** The potential difference \( V \) across the terminals of the source when current flows can be expressed as:
\[
V = \text{EMF} - I \times r
\]
- **Explanation:** Here, \( I \times r \) represents the voltage lost due to internal resistance. Therefore, the potential difference \( V \) is always less than the EMF due to this internal voltage drop.
### **Summary**
- **EMF** is the maximum voltage that a source can provide when no current is flowing.
- **Potential Difference** across the terminals of the source when current flows is less than the EMF because of the internal resistance of the source.
- In summary, the internal resistance of real sources causes a drop in the voltage that appears across the terminals when current is flowing, making the potential difference less than the EMF.
Understanding these concepts is crucial for analyzing and designing electrical circuits, as it helps in accounting for real-world factors that affect the performance of electrical components and sources.
### **Definitions**
1. **Electromotive Force (EMF):**
- **Definition:** EMF is a measure of the energy provided by a source of electrical energy, such as a battery or generator, per unit charge. It represents the maximum potential difference between the terminals of the source when no current is flowing.
- **Source of Energy:** EMF is generated by converting different forms of energy (chemical, mechanical, etc.) into electrical energy.
2. **Potential Difference (PD):**
- **Definition:** PD, also known as voltage, is the actual voltage across a component or between two points in a circuit when current is flowing. It is the work done per unit charge to move a charge from one point to another in the circuit.
- **Dependence on Circuit:** PD varies depending on the circuit components and their resistance.
### **Comparison and Explanation**
1. **Ideal vs. Real Conditions:**
- **Ideal Case (No Current):** In an ideal case where no current flows, the potential difference across the terminals of a source equals its EMF. For example, in a disconnected battery, the voltage you measure is the EMF.
- **Real Case (With Current):** When the circuit is closed and current flows, the potential difference across the terminals of the source can be less than the EMF. This reduction is due to the internal resistance of the source.
2. **Internal Resistance:**
- **Internal Resistance (r):** Real sources like batteries have an internal resistance. This resistance causes a voltage drop within the source when current flows. The EMF is the voltage that the source would provide if it had no internal resistance, while the potential difference is reduced by the voltage drop across the internal resistance.
- **Voltage Drop (I × r):** The voltage drop across the internal resistance can be calculated as \( I \times r \), where \( I \) is the current and \( r \) is the internal resistance.
3. **Relationship Between EMF and PD:**
- **Equation:** The potential difference \( V \) across the terminals of the source when current flows can be expressed as:
\[
V = \text{EMF} - I \times r
\]
- **Explanation:** Here, \( I \times r \) represents the voltage lost due to internal resistance. Therefore, the potential difference \( V \) is always less than the EMF due to this internal voltage drop.
### **Summary**
- **EMF** is the maximum voltage that a source can provide when no current is flowing.
- **Potential Difference** across the terminals of the source when current flows is less than the EMF because of the internal resistance of the source.
- In summary, the internal resistance of real sources causes a drop in the voltage that appears across the terminals when current is flowing, making the potential difference less than the EMF.
Understanding these concepts is crucial for analyzing and designing electrical circuits, as it helps in accounting for real-world factors that affect the performance of electrical components and sources.
Electromotive Force (EMF) and potential difference are related concepts in electrical circuits, but they are not always equal. Understanding the difference between them requires a bit of exploration into what each term means and the contexts in which they are used.
### **Electromotive Force (EMF)**
1. **Definition**: EMF is the maximum potential difference that a source (like a battery or generator) can provide when no current is flowing. It represents the energy provided by the source per unit charge. EMF is essentially the work done by the source to move a unit charge from one terminal to the other.
2. **Source Characteristics**: The EMF of a source is a property of the source itself. For instance, a battery with an EMF of 12 volts means it can provide a maximum of 12 volts of potential difference when not connected to a circuit or when no current flows.
3. **Internal Resistance**: Real sources have internal resistance, which causes a difference between the EMF and the actual potential difference across the terminals when a current is flowing. This internal resistance can affect the actual voltage that appears across the terminals when the source is under load.
### **Potential Difference (Voltage)**
1. **Definition**: Potential difference, also known as voltage, is the difference in electric potential between two points in a circuit. It can be measured across any two points where charges are present and can be defined for parts of a circuit, such as across a resistor.
2. **Load Conditions**: When current flows through a circuit, the potential difference across the terminals of a source is generally less than the EMF due to the internal resistance of the source. The actual voltage across the terminals is what is observed in practical situations.
### **Relationship Between EMF and Potential Difference**
1. **Internal Resistance Effect**: The internal resistance of the source affects the potential difference across its terminals. If \( R_{\text{int}} \) is the internal resistance of the source and \( I \) is the current flowing through the circuit, then the potential difference \( V \) across the terminals is given by:
\[
V = \text{EMF} - I \cdot R_{\text{int}}
\]
This equation shows that the potential difference \( V \) is less than the EMF by an amount equal to the product of the current and the internal resistance.
2. **Circuit Example**: For instance, if you have a battery with an EMF of 12 volts and it has an internal resistance of 1 ohm, and the current flowing through the circuit is 2 amperes, the potential difference across the terminals of the battery is:
\[
V = 12\, \text{V} - (2\, \text{A} \times 1\, \Omega) = 12\, \text{V} - 2\, \text{V} = 10\, \text{V}
\]
Here, the potential difference is 10 volts, which is less than the EMF of 12 volts due to the voltage drop across the internal resistance.
### **Summary**
- **EMF** is the maximum potential difference a source can provide when no current is flowing.
- **Potential Difference** across a source when it is in use (with current flowing) is less than the EMF due to the internal resistance of the source.
- The difference between EMF and potential difference arises because the internal resistance of the source causes a drop in voltage when current flows.
In essence, EMF represents the ideal, maximum voltage available, while the potential difference is the actual voltage you measure across the terminals when the source is connected to a circuit and current is flowing.
### **Electromotive Force (EMF)**
1. **Definition**: EMF is the maximum potential difference that a source (like a battery or generator) can provide when no current is flowing. It represents the energy provided by the source per unit charge. EMF is essentially the work done by the source to move a unit charge from one terminal to the other.
2. **Source Characteristics**: The EMF of a source is a property of the source itself. For instance, a battery with an EMF of 12 volts means it can provide a maximum of 12 volts of potential difference when not connected to a circuit or when no current flows.
3. **Internal Resistance**: Real sources have internal resistance, which causes a difference between the EMF and the actual potential difference across the terminals when a current is flowing. This internal resistance can affect the actual voltage that appears across the terminals when the source is under load.
### **Potential Difference (Voltage)**
1. **Definition**: Potential difference, also known as voltage, is the difference in electric potential between two points in a circuit. It can be measured across any two points where charges are present and can be defined for parts of a circuit, such as across a resistor.
2. **Load Conditions**: When current flows through a circuit, the potential difference across the terminals of a source is generally less than the EMF due to the internal resistance of the source. The actual voltage across the terminals is what is observed in practical situations.
### **Relationship Between EMF and Potential Difference**
1. **Internal Resistance Effect**: The internal resistance of the source affects the potential difference across its terminals. If \( R_{\text{int}} \) is the internal resistance of the source and \( I \) is the current flowing through the circuit, then the potential difference \( V \) across the terminals is given by:
\[
V = \text{EMF} - I \cdot R_{\text{int}}
\]
This equation shows that the potential difference \( V \) is less than the EMF by an amount equal to the product of the current and the internal resistance.
2. **Circuit Example**: For instance, if you have a battery with an EMF of 12 volts and it has an internal resistance of 1 ohm, and the current flowing through the circuit is 2 amperes, the potential difference across the terminals of the battery is:
\[
V = 12\, \text{V} - (2\, \text{A} \times 1\, \Omega) = 12\, \text{V} - 2\, \text{V} = 10\, \text{V}
\]
Here, the potential difference is 10 volts, which is less than the EMF of 12 volts due to the voltage drop across the internal resistance.
### **Summary**
- **EMF** is the maximum potential difference a source can provide when no current is flowing.
- **Potential Difference** across a source when it is in use (with current flowing) is less than the EMF due to the internal resistance of the source.
- The difference between EMF and potential difference arises because the internal resistance of the source causes a drop in voltage when current flows.
In essence, EMF represents the ideal, maximum voltage available, while the potential difference is the actual voltage you measure across the terminals when the source is connected to a circuit and current is flowing.