Why is the emf of a cell always greater than its terminal voltage?
2 Answers
The electromotive force (EMF) of a cell is always greater than its terminal voltage due to the **internal resistance** of the cell. To understand why this happens, let's break it down:
### 1. **EMF of a Cell:**
The EMF (Electromotive Force) of a cell is the maximum potential difference between the two terminals of the cell when no current is flowing through the circuit. It represents the energy provided by the cell to move a unit charge from the negative terminal to the positive terminal inside the cell. In simpler terms, EMF is the "ideal" voltage of the cell when it is not connected to any load.
### 2. **Terminal Voltage:**
The terminal voltage is the actual voltage available at the terminals of the cell when it is connected to a circuit, i.e., when current is flowing. This is the voltage that can be measured across the cell’s terminals when it is supplying power to an external load.
### 3. **Internal Resistance:**
All real-world cells and batteries have some amount of **internal resistance (r)**, which is due to the materials inside the battery and how they resist the flow of electric current. When the cell is connected to an external circuit, current flows, and this internal resistance causes a voltage drop within the cell.
### 4. **Voltage Drop Across Internal Resistance:**
When the cell is delivering current, some of the energy supplied by the cell is lost inside the cell due to its internal resistance. The voltage drop across the internal resistance is given by Ohm’s Law as:
\[
V_{\text{drop}} = I \times r
\]
Where:
- \( V_{\text{drop}} \) = voltage drop due to internal resistance,
- \( I \) = current flowing through the circuit,
- \( r \) = internal resistance of the cell.
This voltage drop reduces the effective voltage available at the terminals of the cell.
### 5. **Relation Between EMF, Terminal Voltage, and Internal Resistance:**
When the cell is delivering current, the terminal voltage (V) can be related to the EMF (\(E\)) and the internal resistance as:
\[
V = E - I \times r
\]
Where:
- \( V \) = terminal voltage,
- \( E \) = EMF of the cell,
- \( I \) = current through the circuit,
- \( r \) = internal resistance of the cell.
As you can see, the terminal voltage \( V \) is always less than the EMF \( E \) by the amount of \( I \times r \). This difference is the voltage drop across the internal resistance.
### 6. **Why is EMF Greater than Terminal Voltage?**
- When the cell is **not delivering any current** (open circuit condition, \( I = 0 \)), the terminal voltage equals the EMF, because no voltage is lost across the internal resistance.
- When the cell is **delivering current** (under load), some of the energy is dissipated within the cell itself due to its internal resistance, causing a reduction in the terminal voltage. The more current that flows, the larger the voltage drop across the internal resistance, and the bigger the difference between the EMF and the terminal voltage.
Thus, under normal operating conditions (when the cell is powering a circuit), the EMF of the cell is greater than the terminal voltage because part of the EMF is used to overcome the internal resistance of the cell.
### Summary:
The EMF of a cell is always greater than its terminal voltage because, when current flows, some of the energy provided by the cell is lost internally due to the cell's internal resistance. The terminal voltage is the EMF minus the voltage drop caused by this internal resistance. Therefore, in any real cell, the terminal voltage is always less than the EMF unless the cell is in an open circuit (no current flowing).
### 1. **EMF of a Cell:**
The EMF (Electromotive Force) of a cell is the maximum potential difference between the two terminals of the cell when no current is flowing through the circuit. It represents the energy provided by the cell to move a unit charge from the negative terminal to the positive terminal inside the cell. In simpler terms, EMF is the "ideal" voltage of the cell when it is not connected to any load.
### 2. **Terminal Voltage:**
The terminal voltage is the actual voltage available at the terminals of the cell when it is connected to a circuit, i.e., when current is flowing. This is the voltage that can be measured across the cell’s terminals when it is supplying power to an external load.
### 3. **Internal Resistance:**
All real-world cells and batteries have some amount of **internal resistance (r)**, which is due to the materials inside the battery and how they resist the flow of electric current. When the cell is connected to an external circuit, current flows, and this internal resistance causes a voltage drop within the cell.
### 4. **Voltage Drop Across Internal Resistance:**
When the cell is delivering current, some of the energy supplied by the cell is lost inside the cell due to its internal resistance. The voltage drop across the internal resistance is given by Ohm’s Law as:
\[
V_{\text{drop}} = I \times r
\]
Where:
- \( V_{\text{drop}} \) = voltage drop due to internal resistance,
- \( I \) = current flowing through the circuit,
- \( r \) = internal resistance of the cell.
This voltage drop reduces the effective voltage available at the terminals of the cell.
### 5. **Relation Between EMF, Terminal Voltage, and Internal Resistance:**
When the cell is delivering current, the terminal voltage (V) can be related to the EMF (\(E\)) and the internal resistance as:
\[
V = E - I \times r
\]
Where:
- \( V \) = terminal voltage,
- \( E \) = EMF of the cell,
- \( I \) = current through the circuit,
- \( r \) = internal resistance of the cell.
As you can see, the terminal voltage \( V \) is always less than the EMF \( E \) by the amount of \( I \times r \). This difference is the voltage drop across the internal resistance.
### 6. **Why is EMF Greater than Terminal Voltage?**
- When the cell is **not delivering any current** (open circuit condition, \( I = 0 \)), the terminal voltage equals the EMF, because no voltage is lost across the internal resistance.
- When the cell is **delivering current** (under load), some of the energy is dissipated within the cell itself due to its internal resistance, causing a reduction in the terminal voltage. The more current that flows, the larger the voltage drop across the internal resistance, and the bigger the difference between the EMF and the terminal voltage.
Thus, under normal operating conditions (when the cell is powering a circuit), the EMF of the cell is greater than the terminal voltage because part of the EMF is used to overcome the internal resistance of the cell.
### Summary:
The EMF of a cell is always greater than its terminal voltage because, when current flows, some of the energy provided by the cell is lost internally due to the cell's internal resistance. The terminal voltage is the EMF minus the voltage drop caused by this internal resistance. Therefore, in any real cell, the terminal voltage is always less than the EMF unless the cell is in an open circuit (no current flowing).
To understand why the electromotive force (EMF) of a cell is always greater than its terminal voltage, we need to delve into the concepts of EMF, terminal voltage, and internal resistance.
### Definitions
1. **Electromotive Force (EMF)**:
- EMF is the maximum potential difference between the terminals of a cell when no current is flowing through it. It's essentially the energy provided per unit charge by the cell's chemical reaction to drive current through an external circuit.
2. **Terminal Voltage**:
- Terminal voltage is the actual voltage measured across the terminals of a cell when current is flowing. This is the voltage you observe when the cell is in use in a circuit.
3. **Internal Resistance**:
- Internal resistance is the resistance within the cell itself that opposes the flow of current. This resistance is due to the materials and reactions inside the cell.
### Relationship Between EMF and Terminal Voltage
When a cell is delivering current to an external circuit, the terminal voltage is affected by the internal resistance of the cell. The relationship between the EMF (\( \mathcal{E} \)), terminal voltage (\( V \)), and internal resistance (\( r \)) can be expressed by the following formula:
\[ V = \mathcal{E} - I \cdot r \]
where:
- \( I \) is the current flowing through the circuit.
- \( r \) is the internal resistance of the cell.
### Why EMF Is Always Greater Than Terminal Voltage
1. **Internal Resistance Drop**:
- When current flows through the cell, some of the electrical energy is dissipated as heat due to the internal resistance. This causes a voltage drop inside the cell. The greater the current, the larger the voltage drop across the internal resistance. This means the voltage available at the terminals (terminal voltage) will be less than the EMF of the cell.
2. **No-Load Condition**:
- Under no-load conditions (when no current is flowing), the terminal voltage equals the EMF of the cell. This is because there’s no internal resistance drop. However, as soon as current flows, the internal resistance causes a reduction in the terminal voltage relative to the EMF.
3. **Practical Example**:
- Imagine a battery with an EMF of 12V and an internal resistance of 1 ohm. If a current of 2A is flowing through the circuit, the voltage drop across the internal resistance is \( I \cdot r = 2 \text{A} \times 1 \text{Ω} = 2 \text{V} \). Therefore, the terminal voltage \( V \) is \( \mathcal{E} - I \cdot r = 12 \text{V} - 2 \text{V} = 10 \text{V} \).
In summary, the EMF of a cell is always greater than its terminal voltage when current is flowing because of the internal resistance causing a voltage drop within the cell. The terminal voltage is the EMF minus the voltage drop across the internal resistance.
### Definitions
1. **Electromotive Force (EMF)**:
- EMF is the maximum potential difference between the terminals of a cell when no current is flowing through it. It's essentially the energy provided per unit charge by the cell's chemical reaction to drive current through an external circuit.
2. **Terminal Voltage**:
- Terminal voltage is the actual voltage measured across the terminals of a cell when current is flowing. This is the voltage you observe when the cell is in use in a circuit.
3. **Internal Resistance**:
- Internal resistance is the resistance within the cell itself that opposes the flow of current. This resistance is due to the materials and reactions inside the cell.
### Relationship Between EMF and Terminal Voltage
When a cell is delivering current to an external circuit, the terminal voltage is affected by the internal resistance of the cell. The relationship between the EMF (\( \mathcal{E} \)), terminal voltage (\( V \)), and internal resistance (\( r \)) can be expressed by the following formula:
\[ V = \mathcal{E} - I \cdot r \]
where:
- \( I \) is the current flowing through the circuit.
- \( r \) is the internal resistance of the cell.
### Why EMF Is Always Greater Than Terminal Voltage
1. **Internal Resistance Drop**:
- When current flows through the cell, some of the electrical energy is dissipated as heat due to the internal resistance. This causes a voltage drop inside the cell. The greater the current, the larger the voltage drop across the internal resistance. This means the voltage available at the terminals (terminal voltage) will be less than the EMF of the cell.
2. **No-Load Condition**:
- Under no-load conditions (when no current is flowing), the terminal voltage equals the EMF of the cell. This is because there’s no internal resistance drop. However, as soon as current flows, the internal resistance causes a reduction in the terminal voltage relative to the EMF.
3. **Practical Example**:
- Imagine a battery with an EMF of 12V and an internal resistance of 1 ohm. If a current of 2A is flowing through the circuit, the voltage drop across the internal resistance is \( I \cdot r = 2 \text{A} \times 1 \text{Ω} = 2 \text{V} \). Therefore, the terminal voltage \( V \) is \( \mathcal{E} - I \cdot r = 12 \text{V} - 2 \text{V} = 10 \text{V} \).
In summary, the EMF of a cell is always greater than its terminal voltage when current is flowing because of the internal resistance causing a voltage drop within the cell. The terminal voltage is the EMF minus the voltage drop across the internal resistance.