Why the emf of a cell is always greater than its terminal potential difference?
2 Answers
The electromotive force (emf) of a cell is always greater than its terminal potential difference due to the internal resistance of the cell. Here's a detailed explanation:
### **Definitions**
1. **Electromotive Force (emf):** This is the maximum potential difference that a cell or battery can provide when no current is flowing through the circuit. It's the measure of the energy per unit charge provided by the cell’s chemical reactions.
2. **Terminal Potential Difference (TPD):** This is the potential difference across the terminals of the cell when it is supplying current to the external circuit. It is the voltage you measure across the cell's terminals when the circuit is closed and current flows.
### **Why Emf is Greater Than Terminal Potential Difference**
When a cell is connected to a circuit, it supplies current, and the following factors come into play:
1. **Internal Resistance (r):** Every real cell has some internal resistance due to the materials and construction of the cell. This resistance causes a voltage drop inside the cell as current flows.
2. **Current (I):** When current flows through the cell, a voltage drop occurs across the internal resistance of the cell. This can be described using Ohm's law: \( V = IR \), where \( R \) is the resistance and \( I \) is the current.
### **Mathematical Explanation**
The relationship between emf (\( \mathcal{E} \)), terminal potential difference (V), internal resistance (r), and current (I) can be described by the following equations:
1. **Emf Equation:**
\[ \mathcal{E} = V + Ir \]
Here, \( \mathcal{E} \) is the emf, \( V \) is the terminal potential difference, \( I \) is the current, and \( r \) is the internal resistance.
2. **Terminal Potential Difference:**
\[ V = \mathcal{E} - Ir \]
This equation shows that the terminal potential difference is less than the emf by the amount of the voltage drop caused by the internal resistance.
### **Explanation**
- **No Current Flow:** When no current flows (open circuit), the terminal potential difference equals the emf, as there’s no internal voltage drop.
- **Current Flow:** When current flows (closed circuit), the internal resistance causes a voltage drop, reducing the terminal potential difference below the emf. Specifically, the terminal potential difference is the emf minus the voltage drop across the internal resistance: \( V = \mathcal{E} - Ir \).
### **Summary**
The emf of a cell represents its maximum potential difference when not under load, while the terminal potential difference is the actual voltage available when current is drawn. The difference arises due to the internal resistance of the cell, which causes a voltage drop as current flows. Thus, the emf is always greater than the terminal potential difference in practical situations.
### **Definitions**
1. **Electromotive Force (emf):** This is the maximum potential difference that a cell or battery can provide when no current is flowing through the circuit. It's the measure of the energy per unit charge provided by the cell’s chemical reactions.
2. **Terminal Potential Difference (TPD):** This is the potential difference across the terminals of the cell when it is supplying current to the external circuit. It is the voltage you measure across the cell's terminals when the circuit is closed and current flows.
### **Why Emf is Greater Than Terminal Potential Difference**
When a cell is connected to a circuit, it supplies current, and the following factors come into play:
1. **Internal Resistance (r):** Every real cell has some internal resistance due to the materials and construction of the cell. This resistance causes a voltage drop inside the cell as current flows.
2. **Current (I):** When current flows through the cell, a voltage drop occurs across the internal resistance of the cell. This can be described using Ohm's law: \( V = IR \), where \( R \) is the resistance and \( I \) is the current.
### **Mathematical Explanation**
The relationship between emf (\( \mathcal{E} \)), terminal potential difference (V), internal resistance (r), and current (I) can be described by the following equations:
1. **Emf Equation:**
\[ \mathcal{E} = V + Ir \]
Here, \( \mathcal{E} \) is the emf, \( V \) is the terminal potential difference, \( I \) is the current, and \( r \) is the internal resistance.
2. **Terminal Potential Difference:**
\[ V = \mathcal{E} - Ir \]
This equation shows that the terminal potential difference is less than the emf by the amount of the voltage drop caused by the internal resistance.
### **Explanation**
- **No Current Flow:** When no current flows (open circuit), the terminal potential difference equals the emf, as there’s no internal voltage drop.
- **Current Flow:** When current flows (closed circuit), the internal resistance causes a voltage drop, reducing the terminal potential difference below the emf. Specifically, the terminal potential difference is the emf minus the voltage drop across the internal resistance: \( V = \mathcal{E} - Ir \).
### **Summary**
The emf of a cell represents its maximum potential difference when not under load, while the terminal potential difference is the actual voltage available when current is drawn. The difference arises due to the internal resistance of the cell, which causes a voltage drop as current flows. Thus, the emf is always greater than the terminal potential difference in practical situations.
The electromotive force (EMF) of a cell is always greater than its terminal potential difference due to the internal resistance of the cell. To understand this better, let’s break it down:
### 1. **Definition of EMF and Terminal Potential Difference**
- **EMF (Electromotive Force)**: This is the maximum potential difference a cell can provide when no current is flowing through it. It represents the work done by the cell in moving a unit charge from one terminal to another within the cell itself.
- **Terminal Potential Difference**: This is the actual voltage available at the terminals of the cell when it is supplying current to an external circuit. It is the potential difference measured across the terminals under load conditions.
### 2. **Internal Resistance and Its Effect**
Cells have an internal resistance (r) which affects the terminal potential difference. When a current (I) flows through the cell, a voltage drop occurs across this internal resistance.
The relationship between EMF (\( \mathcal{E} \)), terminal potential difference (V), and internal resistance (r) is given by:
\[ V = \mathcal{E} - Ir \]
Here’s a step-by-step explanation:
1. **Internal Resistance**: Every real cell has some internal resistance due to the materials and design of the cell. When current flows, this resistance causes a voltage drop within the cell.
2. **Voltage Drop**: The internal resistance creates a voltage drop (\( Ir \)) inside the cell. This drop reduces the voltage available at the cell terminals compared to the EMF.
3. **Terminal Potential Difference**: The voltage you measure across the terminals of the cell when it is connected to a circuit (i.e., when it is delivering current) is less than the EMF. This is because the terminal voltage is the EMF minus the internal voltage drop (\( Ir \)).
### 3. **Practical Example**
Consider a cell with an EMF of 12V and an internal resistance of 2 ohms. If the cell is delivering a current of 1A to an external circuit, the voltage drop across the internal resistance is:
\[ \text{Voltage drop} = I \times r = 1 \, \text{A} \times 2 \, \text{ohms} = 2 \, \text{V} \]
So, the terminal potential difference (V) is:
\[ V = \mathcal{E} - Ir = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V} \]
In this case, the EMF (12V) is indeed greater than the terminal potential difference (10V) by the amount of the internal voltage drop.
### 4. **Summary**
The EMF of a cell is always greater than its terminal potential difference because the internal resistance of the cell causes a voltage drop when current flows. This drop reduces the voltage measured across the terminals, which is why the terminal potential difference is less than the EMF.
### 1. **Definition of EMF and Terminal Potential Difference**
- **EMF (Electromotive Force)**: This is the maximum potential difference a cell can provide when no current is flowing through it. It represents the work done by the cell in moving a unit charge from one terminal to another within the cell itself.
- **Terminal Potential Difference**: This is the actual voltage available at the terminals of the cell when it is supplying current to an external circuit. It is the potential difference measured across the terminals under load conditions.
### 2. **Internal Resistance and Its Effect**
Cells have an internal resistance (r) which affects the terminal potential difference. When a current (I) flows through the cell, a voltage drop occurs across this internal resistance.
The relationship between EMF (\( \mathcal{E} \)), terminal potential difference (V), and internal resistance (r) is given by:
\[ V = \mathcal{E} - Ir \]
Here’s a step-by-step explanation:
1. **Internal Resistance**: Every real cell has some internal resistance due to the materials and design of the cell. When current flows, this resistance causes a voltage drop within the cell.
2. **Voltage Drop**: The internal resistance creates a voltage drop (\( Ir \)) inside the cell. This drop reduces the voltage available at the cell terminals compared to the EMF.
3. **Terminal Potential Difference**: The voltage you measure across the terminals of the cell when it is connected to a circuit (i.e., when it is delivering current) is less than the EMF. This is because the terminal voltage is the EMF minus the internal voltage drop (\( Ir \)).
### 3. **Practical Example**
Consider a cell with an EMF of 12V and an internal resistance of 2 ohms. If the cell is delivering a current of 1A to an external circuit, the voltage drop across the internal resistance is:
\[ \text{Voltage drop} = I \times r = 1 \, \text{A} \times 2 \, \text{ohms} = 2 \, \text{V} \]
So, the terminal potential difference (V) is:
\[ V = \mathcal{E} - Ir = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V} \]
In this case, the EMF (12V) is indeed greater than the terminal potential difference (10V) by the amount of the internal voltage drop.
### 4. **Summary**
The EMF of a cell is always greater than its terminal potential difference because the internal resistance of the cell causes a voltage drop when current flows. This drop reduces the voltage measured across the terminals, which is why the terminal potential difference is less than the EMF.