Why terminal potential is less than the emf of a cell?
2 Answers
The terminal potential of a cell, often referred to as the terminal voltage, is usually less than the electromotive force (EMF) of the cell due to a phenomenon known as voltage drop. This drop occurs primarily due to internal resistance within the cell. To understand this concept in detail, we’ll explore what EMF is, the concept of terminal potential, and the factors contributing to the difference between them.
### 1. Definitions
**Electromotive Force (EMF)**:
- EMF is the maximum potential difference that a cell can provide when no current is flowing. It is essentially the energy per unit charge provided by the cell, measured in volts (V). EMF is the ideal voltage that one would expect from the cell if it were perfectly efficient.
**Terminal Potential (or Terminal Voltage)**:
- Terminal potential is the voltage measured across the terminals of the cell when it is supplying current to an external circuit. This value reflects the actual voltage available to do work in the circuit.
### 2. Understanding the Difference
The relationship between EMF (E), terminal potential (V), current (I), and internal resistance (r) can be described by the formula:
\[
V = E - I \cdot r
\]
Where:
- \( V \) = terminal potential (voltage across the terminals when the current is flowing)
- \( E \) = EMF of the cell (no load condition)
- \( I \) = current flowing through the circuit
- \( r \) = internal resistance of the cell
### 3. Reasons Why Terminal Potential is Less Than EMF
#### **A. Internal Resistance**
- All real batteries and cells have some internal resistance due to the materials and chemical processes occurring within them. This resistance leads to a voltage drop when current flows through the cell.
#### **B. Ohm's Law**
- According to Ohm's Law (\( V = I \cdot R \)), any resistance in the circuit, including internal resistance, will cause a drop in voltage. When current \( I \) flows through the internal resistance \( r \) of the cell, a portion of the total EMF is "used up" in overcoming this internal resistance.
#### **C. Load Condition**
- When a cell is under load (when it is connected to an external circuit and current is flowing), the terminal voltage decreases. This is because a part of the energy provided by the cell is expended to overcome the internal resistance. The more current drawn from the cell, the larger the voltage drop due to internal resistance.
### 4. Practical Example
Let’s consider a simple example:
- Suppose a battery has an EMF of 12 V and an internal resistance of 1 ohm.
- If a current of 2 A is drawn from the battery, the voltage drop due to internal resistance can be calculated as:
\[
\text{Voltage drop} = I \cdot r = 2 \, \text{A} \cdot 1 \, \Omega = 2 \, \text{V}
\]
- The terminal potential (V) when the current is flowing would then be:
\[
V = E - I \cdot r = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V}
\]
In this scenario, the terminal potential is 10 V, which is less than the EMF of 12 V due to the voltage drop caused by the internal resistance.
### 5. Implications
- **Efficiency**: The difference between EMF and terminal potential indicates that not all of the energy produced by the cell is available for external work. The internal resistance leads to energy loss in the form of heat.
- **Battery Performance**: Understanding the relationship helps in designing batteries for specific applications, considering factors like discharge rates and internal resistance to minimize energy loss.
### 6. Conclusion
In summary, the terminal potential of a cell is less than its EMF primarily due to the internal resistance of the cell. When current flows, this internal resistance causes a voltage drop, reducing the voltage available at the terminals. This relationship is essential for understanding how batteries perform under load and helps in improving the design and efficiency of energy storage devices.
### 1. Definitions
**Electromotive Force (EMF)**:
- EMF is the maximum potential difference that a cell can provide when no current is flowing. It is essentially the energy per unit charge provided by the cell, measured in volts (V). EMF is the ideal voltage that one would expect from the cell if it were perfectly efficient.
**Terminal Potential (or Terminal Voltage)**:
- Terminal potential is the voltage measured across the terminals of the cell when it is supplying current to an external circuit. This value reflects the actual voltage available to do work in the circuit.
### 2. Understanding the Difference
The relationship between EMF (E), terminal potential (V), current (I), and internal resistance (r) can be described by the formula:
\[
V = E - I \cdot r
\]
Where:
- \( V \) = terminal potential (voltage across the terminals when the current is flowing)
- \( E \) = EMF of the cell (no load condition)
- \( I \) = current flowing through the circuit
- \( r \) = internal resistance of the cell
### 3. Reasons Why Terminal Potential is Less Than EMF
#### **A. Internal Resistance**
- All real batteries and cells have some internal resistance due to the materials and chemical processes occurring within them. This resistance leads to a voltage drop when current flows through the cell.
#### **B. Ohm's Law**
- According to Ohm's Law (\( V = I \cdot R \)), any resistance in the circuit, including internal resistance, will cause a drop in voltage. When current \( I \) flows through the internal resistance \( r \) of the cell, a portion of the total EMF is "used up" in overcoming this internal resistance.
#### **C. Load Condition**
- When a cell is under load (when it is connected to an external circuit and current is flowing), the terminal voltage decreases. This is because a part of the energy provided by the cell is expended to overcome the internal resistance. The more current drawn from the cell, the larger the voltage drop due to internal resistance.
### 4. Practical Example
Let’s consider a simple example:
- Suppose a battery has an EMF of 12 V and an internal resistance of 1 ohm.
- If a current of 2 A is drawn from the battery, the voltage drop due to internal resistance can be calculated as:
\[
\text{Voltage drop} = I \cdot r = 2 \, \text{A} \cdot 1 \, \Omega = 2 \, \text{V}
\]
- The terminal potential (V) when the current is flowing would then be:
\[
V = E - I \cdot r = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V}
\]
In this scenario, the terminal potential is 10 V, which is less than the EMF of 12 V due to the voltage drop caused by the internal resistance.
### 5. Implications
- **Efficiency**: The difference between EMF and terminal potential indicates that not all of the energy produced by the cell is available for external work. The internal resistance leads to energy loss in the form of heat.
- **Battery Performance**: Understanding the relationship helps in designing batteries for specific applications, considering factors like discharge rates and internal resistance to minimize energy loss.
### 6. Conclusion
In summary, the terminal potential of a cell is less than its EMF primarily due to the internal resistance of the cell. When current flows, this internal resistance causes a voltage drop, reducing the voltage available at the terminals. This relationship is essential for understanding how batteries perform under load and helps in improving the design and efficiency of energy storage devices.
The terminal potential of a cell (or battery) is often less than its electromotive force (EMF) due to the internal resistance of the cell. Here’s a detailed explanation:
### 1. **Definitions**
- **Electromotive Force (EMF):** This is the maximum potential difference between the terminals of the cell when no current is flowing. It is essentially the voltage generated by the cell due to chemical reactions occurring within it.
- **Terminal Potential:** This is the actual potential difference across the terminals of the cell when it is delivering current to an external circuit.
### 2. **Internal Resistance**
Every cell has some internal resistance, which can be attributed to the resistive components within the cell, such as the electrolyte, the electrodes, and the connections between them. This internal resistance causes a voltage drop when current flows through the cell.
### 3. **Relationship Between EMF and Terminal Potential**
When a cell is delivering current to a load, the internal resistance causes a voltage drop inside the cell. This drop reduces the voltage available at the terminals of the cell. The relationship between EMF (E), terminal potential (V), current (I), and internal resistance (r) is given by:
\[ V = E - I \cdot r \]
Here’s what happens in detail:
- **Internal Voltage Drop:** As current flows through the internal resistance of the cell, it creates a voltage drop according to Ohm's Law. This drop is equal to \( I \cdot r \), where \( I \) is the current and \( r \) is the internal resistance.
- **Actual Terminal Potential:** The voltage measured across the terminals (terminal potential) is the EMF minus this internal voltage drop.
### 4. **Impact of Internal Resistance**
- **High Internal Resistance:** Cells with high internal resistance will have a significant drop in terminal potential when a current is drawn. This is particularly noticeable when the cell is providing a high current.
- **Low Internal Resistance:** Cells designed with low internal resistance (like many modern batteries) will have a smaller voltage drop and hence a terminal potential closer to the EMF, even under load.
### 5. **Practical Implications**
- **Battery Performance:** In practical applications, understanding the internal resistance is crucial for battery performance. High internal resistance can lead to significant voltage drops, reducing the efficiency and performance of the cell in powering devices.
- **Design Considerations:** Engineers and designers often focus on minimizing internal resistance to maximize the efficiency of batteries, especially for applications requiring high currents or long-term reliability.
In summary, the terminal potential of a cell is less than its EMF because the internal resistance of the cell causes a voltage drop when current flows. The actual voltage you measure at the terminals depends on both the EMF of the cell and the current flowing through its internal resistance.
### 1. **Definitions**
- **Electromotive Force (EMF):** This is the maximum potential difference between the terminals of the cell when no current is flowing. It is essentially the voltage generated by the cell due to chemical reactions occurring within it.
- **Terminal Potential:** This is the actual potential difference across the terminals of the cell when it is delivering current to an external circuit.
### 2. **Internal Resistance**
Every cell has some internal resistance, which can be attributed to the resistive components within the cell, such as the electrolyte, the electrodes, and the connections between them. This internal resistance causes a voltage drop when current flows through the cell.
### 3. **Relationship Between EMF and Terminal Potential**
When a cell is delivering current to a load, the internal resistance causes a voltage drop inside the cell. This drop reduces the voltage available at the terminals of the cell. The relationship between EMF (E), terminal potential (V), current (I), and internal resistance (r) is given by:
\[ V = E - I \cdot r \]
Here’s what happens in detail:
- **Internal Voltage Drop:** As current flows through the internal resistance of the cell, it creates a voltage drop according to Ohm's Law. This drop is equal to \( I \cdot r \), where \( I \) is the current and \( r \) is the internal resistance.
- **Actual Terminal Potential:** The voltage measured across the terminals (terminal potential) is the EMF minus this internal voltage drop.
### 4. **Impact of Internal Resistance**
- **High Internal Resistance:** Cells with high internal resistance will have a significant drop in terminal potential when a current is drawn. This is particularly noticeable when the cell is providing a high current.
- **Low Internal Resistance:** Cells designed with low internal resistance (like many modern batteries) will have a smaller voltage drop and hence a terminal potential closer to the EMF, even under load.
### 5. **Practical Implications**
- **Battery Performance:** In practical applications, understanding the internal resistance is crucial for battery performance. High internal resistance can lead to significant voltage drops, reducing the efficiency and performance of the cell in powering devices.
- **Design Considerations:** Engineers and designers often focus on minimizing internal resistance to maximize the efficiency of batteries, especially for applications requiring high currents or long-term reliability.
In summary, the terminal potential of a cell is less than its EMF because the internal resistance of the cell causes a voltage drop when current flows. The actual voltage you measure at the terminals depends on both the EMF of the cell and the current flowing through its internal resistance.