What is the relationship between emf and terminal potential difference of a source?
2 Answers
The relationship between electromotive force (emf) and the terminal potential difference (also known as the terminal voltage) of a source is an important concept in understanding how electrical sources work, such as batteries and generators.
### Key Definitions
1. **Electromotive Force (emf):** This is the maximum potential difference between the terminals of a source when no current is flowing. It is essentially the energy provided by the source per unit charge. It is a measure of the source’s ability to drive current through a circuit.
2. **Terminal Potential Difference (Terminal Voltage):** This is the actual potential difference measured across the terminals of the source when current is flowing. It is the voltage that you observe in a circuit.
### Relationship
The relationship between emf and terminal potential difference is influenced by the internal resistance of the source. Here’s how they are related:
1. **Internal Resistance:** All real sources of emf have some internal resistance, denoted as \( r \). This internal resistance causes a drop in the potential difference when current flows through the source.
2. **Circuit Relationship:** When a current \( I \) flows through a source with internal resistance \( r \), the terminal potential difference \( V_{terminal} \) is given by:
\[
V_{terminal} = \text{emf} - I \cdot r
\]
This equation shows that the terminal potential difference is less than the emf by an amount equal to the voltage drop across the internal resistance.
### Explanation
1. **When No Current Flows:** If there is no current flowing through the circuit (i.e., the circuit is open), the terminal potential difference is equal to the emf because no voltage is lost across the internal resistance.
2. **When Current Flows:** As current flows through the circuit, the internal resistance causes a voltage drop. The greater the current, the larger this voltage drop, which results in a lower terminal potential difference compared to the emf.
3. **Practical Example:** Consider a battery with an emf of 12 volts and an internal resistance of 1 ohm. If the battery supplies a current of 2 amps to a circuit, the voltage drop across the internal resistance is:
\[
V_{drop} = I \cdot r = 2 \text{ A} \times 1 \text{ Ω} = 2 \text{ V}
\]
Hence, the terminal potential difference is:
\[
V_{terminal} = \text{emf} - V_{drop} = 12 \text{ V} - 2 \text{ V} = 10 \text{ V}
\]
In summary, the emf represents the maximum potential difference a source can provide, while the terminal potential difference is the actual voltage available to the external circuit, which is reduced by the voltage drop across the internal resistance when current flows.
### Key Definitions
1. **Electromotive Force (emf):** This is the maximum potential difference between the terminals of a source when no current is flowing. It is essentially the energy provided by the source per unit charge. It is a measure of the source’s ability to drive current through a circuit.
2. **Terminal Potential Difference (Terminal Voltage):** This is the actual potential difference measured across the terminals of the source when current is flowing. It is the voltage that you observe in a circuit.
### Relationship
The relationship between emf and terminal potential difference is influenced by the internal resistance of the source. Here’s how they are related:
1. **Internal Resistance:** All real sources of emf have some internal resistance, denoted as \( r \). This internal resistance causes a drop in the potential difference when current flows through the source.
2. **Circuit Relationship:** When a current \( I \) flows through a source with internal resistance \( r \), the terminal potential difference \( V_{terminal} \) is given by:
\[
V_{terminal} = \text{emf} - I \cdot r
\]
This equation shows that the terminal potential difference is less than the emf by an amount equal to the voltage drop across the internal resistance.
### Explanation
1. **When No Current Flows:** If there is no current flowing through the circuit (i.e., the circuit is open), the terminal potential difference is equal to the emf because no voltage is lost across the internal resistance.
2. **When Current Flows:** As current flows through the circuit, the internal resistance causes a voltage drop. The greater the current, the larger this voltage drop, which results in a lower terminal potential difference compared to the emf.
3. **Practical Example:** Consider a battery with an emf of 12 volts and an internal resistance of 1 ohm. If the battery supplies a current of 2 amps to a circuit, the voltage drop across the internal resistance is:
\[
V_{drop} = I \cdot r = 2 \text{ A} \times 1 \text{ Ω} = 2 \text{ V}
\]
Hence, the terminal potential difference is:
\[
V_{terminal} = \text{emf} - V_{drop} = 12 \text{ V} - 2 \text{ V} = 10 \text{ V}
\]
In summary, the emf represents the maximum potential difference a source can provide, while the terminal potential difference is the actual voltage available to the external circuit, which is reduced by the voltage drop across the internal resistance when current flows.
The relationship between electromotive force (EMF) and terminal potential difference (TPD) of a source is fundamental in understanding how electrical sources like batteries and generators operate. Here’s a detailed explanation:
### 1. **Electromotive Force (EMF)**
**Definition:**
EMF is a measure of the maximum potential difference that a source (like a battery or generator) can provide when no current is flowing through the circuit. It represents the energy per unit charge provided by the source.
**Key Points:**
- It is the theoretical maximum voltage provided by the source.
- It is measured in volts (V).
- It is determined by the internal chemical or mechanical processes within the source.
### 2. **Terminal Potential Difference (TPD)**
**Definition:**
TPD, also known as the terminal voltage, is the actual voltage output of the source when it is connected to an external circuit and current is flowing. It is the voltage measured across the terminals of the source.
**Key Points:**
- It is the voltage available to the external circuit.
- It can vary depending on the current flowing through the source.
- It is also measured in volts (V).
### 3. **Relationship Between EMF and TPD**
When a source provides power to an external circuit, the current flowing through the circuit creates a voltage drop within the source itself due to its internal resistance. This drop affects the terminal potential difference. The relationship between EMF (\( \mathcal{E} \)) and TPD (\( V \)) can be described by the following equation:
\[ V = \mathcal{E} - I \cdot r \]
where:
- \( V \) is the terminal potential difference (voltage across the terminals).
- \( \mathcal{E} \) is the electromotive force (EMF) of the source.
- \( I \) is the current flowing through the circuit.
- \( r \) is the internal resistance of the source.
### 4. **Explanation**
- **No Current Flowing:** When no current flows (\( I = 0 \)), the terminal potential difference is equal to the EMF of the source. This is because there's no voltage drop across the internal resistance.
- **Current Flowing:** When current flows through the circuit, the terminal potential difference is less than the EMF by the amount of the voltage drop due to internal resistance. This drop is given by \( I \cdot r \). The larger the current, the greater the voltage drop across the internal resistance, and thus, the lower the terminal potential difference.
### 5. **Practical Implications**
In practical terms, if you measure the voltage across a battery or any electrical source while it is supplying current to a circuit, the voltage you measure (TPD) will be lower than the EMF. This difference is due to the internal resistance of the source, which affects how much voltage is available to the external circuit.
In summary, the EMF of a source represents its maximum potential difference under ideal conditions (no current), while the terminal potential difference is what you actually measure across the terminals when the source is supplying current. The difference between these two values is due to the internal resistance of the source.
### 1. **Electromotive Force (EMF)**
**Definition:**
EMF is a measure of the maximum potential difference that a source (like a battery or generator) can provide when no current is flowing through the circuit. It represents the energy per unit charge provided by the source.
**Key Points:**
- It is the theoretical maximum voltage provided by the source.
- It is measured in volts (V).
- It is determined by the internal chemical or mechanical processes within the source.
### 2. **Terminal Potential Difference (TPD)**
**Definition:**
TPD, also known as the terminal voltage, is the actual voltage output of the source when it is connected to an external circuit and current is flowing. It is the voltage measured across the terminals of the source.
**Key Points:**
- It is the voltage available to the external circuit.
- It can vary depending on the current flowing through the source.
- It is also measured in volts (V).
### 3. **Relationship Between EMF and TPD**
When a source provides power to an external circuit, the current flowing through the circuit creates a voltage drop within the source itself due to its internal resistance. This drop affects the terminal potential difference. The relationship between EMF (\( \mathcal{E} \)) and TPD (\( V \)) can be described by the following equation:
\[ V = \mathcal{E} - I \cdot r \]
where:
- \( V \) is the terminal potential difference (voltage across the terminals).
- \( \mathcal{E} \) is the electromotive force (EMF) of the source.
- \( I \) is the current flowing through the circuit.
- \( r \) is the internal resistance of the source.
### 4. **Explanation**
- **No Current Flowing:** When no current flows (\( I = 0 \)), the terminal potential difference is equal to the EMF of the source. This is because there's no voltage drop across the internal resistance.
- **Current Flowing:** When current flows through the circuit, the terminal potential difference is less than the EMF by the amount of the voltage drop due to internal resistance. This drop is given by \( I \cdot r \). The larger the current, the greater the voltage drop across the internal resistance, and thus, the lower the terminal potential difference.
### 5. **Practical Implications**
In practical terms, if you measure the voltage across a battery or any electrical source while it is supplying current to a circuit, the voltage you measure (TPD) will be lower than the EMF. This difference is due to the internal resistance of the source, which affects how much voltage is available to the external circuit.
In summary, the EMF of a source represents its maximum potential difference under ideal conditions (no current), while the terminal potential difference is what you actually measure across the terminals when the source is supplying current. The difference between these two values is due to the internal resistance of the source.