Why the potential difference across the terminals of a cell is less than its emf when a current is drawn from it?
2 Answers
The difference between the electromotive force (emf) of a cell and the potential difference (voltage) across its terminals when a current is drawn can be understood through the concepts of internal resistance and energy loss.
### Key Concepts:
1. **Electromotive Force (emf)**: This is the maximum potential difference generated by a cell when no current is flowing. It represents the cell's ability to do work on charges and is often denoted by the symbol \(E\).
2. **Internal Resistance**: Every real cell has some internal resistance (denoted as \(r\)), which arises from the materials and construction of the cell. This resistance opposes the flow of current inside the cell.
3. **Load Resistance**: When a load (like a resistor) is connected to the cell, it draws current \(I\). The total circuit includes both the internal resistance of the cell and the load resistance.
### The Relationship:
When no current flows (open-circuit condition), the potential difference across the terminals is equal to the emf (\(V = E\)). However, when a current is drawn, the situation changes:
1. **Current Flow**: When a load is connected, current \(I\) starts flowing through the circuit, including through the internal resistance of the cell.
2. **Voltage Drop Due to Internal Resistance**: The current flowing through the internal resistance causes a voltage drop across it, which can be calculated using Ohm’s Law:
\[
V_{\text{internal}} = I \cdot r
\]
Here, \(V_{\text{internal}}\) is the voltage drop across the internal resistance, \(I\) is the current, and \(r\) is the internal resistance.
3. **Potential Difference Across Terminals**: The actual potential difference (\(V\)) across the terminals of the cell while current is flowing can be expressed as:
\[
V = E - I \cdot r
\]
This equation shows that the terminal voltage \(V\) is equal to the emf \(E\) minus the voltage drop due to the internal resistance.
### Summary:
When a current is drawn from a cell, the internal resistance causes a loss of voltage, which results in the terminal voltage being less than the emf. The greater the current drawn, the larger the voltage drop across the internal resistance, leading to a more significant difference between the terminal voltage and the emf.
### Practical Implications:
1. **Battery Performance**: In practical applications, the internal resistance affects how well a battery can perform under load. Batteries with lower internal resistance can deliver higher currents with less voltage drop.
2. **Efficiency**: Understanding this difference is crucial for designing electrical circuits and ensuring that devices operate efficiently. If a device requires a certain voltage, the internal resistance of the power source must be considered to ensure it delivers enough voltage under load.
In summary, the reason the potential difference across the terminals of a cell is less than its emf when current is drawn is primarily due to the internal resistance of the cell, which causes a voltage drop when current flows.
### Key Concepts:
1. **Electromotive Force (emf)**: This is the maximum potential difference generated by a cell when no current is flowing. It represents the cell's ability to do work on charges and is often denoted by the symbol \(E\).
2. **Internal Resistance**: Every real cell has some internal resistance (denoted as \(r\)), which arises from the materials and construction of the cell. This resistance opposes the flow of current inside the cell.
3. **Load Resistance**: When a load (like a resistor) is connected to the cell, it draws current \(I\). The total circuit includes both the internal resistance of the cell and the load resistance.
### The Relationship:
When no current flows (open-circuit condition), the potential difference across the terminals is equal to the emf (\(V = E\)). However, when a current is drawn, the situation changes:
1. **Current Flow**: When a load is connected, current \(I\) starts flowing through the circuit, including through the internal resistance of the cell.
2. **Voltage Drop Due to Internal Resistance**: The current flowing through the internal resistance causes a voltage drop across it, which can be calculated using Ohm’s Law:
\[
V_{\text{internal}} = I \cdot r
\]
Here, \(V_{\text{internal}}\) is the voltage drop across the internal resistance, \(I\) is the current, and \(r\) is the internal resistance.
3. **Potential Difference Across Terminals**: The actual potential difference (\(V\)) across the terminals of the cell while current is flowing can be expressed as:
\[
V = E - I \cdot r
\]
This equation shows that the terminal voltage \(V\) is equal to the emf \(E\) minus the voltage drop due to the internal resistance.
### Summary:
When a current is drawn from a cell, the internal resistance causes a loss of voltage, which results in the terminal voltage being less than the emf. The greater the current drawn, the larger the voltage drop across the internal resistance, leading to a more significant difference between the terminal voltage and the emf.
### Practical Implications:
1. **Battery Performance**: In practical applications, the internal resistance affects how well a battery can perform under load. Batteries with lower internal resistance can deliver higher currents with less voltage drop.
2. **Efficiency**: Understanding this difference is crucial for designing electrical circuits and ensuring that devices operate efficiently. If a device requires a certain voltage, the internal resistance of the power source must be considered to ensure it delivers enough voltage under load.
In summary, the reason the potential difference across the terminals of a cell is less than its emf when current is drawn is primarily due to the internal resistance of the cell, which causes a voltage drop when current flows.
The potential difference across the terminals of a cell is less than its electromotive force (EMF) when a current is drawn because of the internal resistance of the cell. Here’s a detailed explanation:
### EMF and Internal Resistance
1. **EMF of a Cell:**
- The EMF of a cell is the maximum potential difference between its terminals when no current is flowing. It represents the work done per unit charge by the cell in moving the charge from one terminal to the other inside the cell.
2. **Internal Resistance:**
- Inside the cell, there is an internal resistance denoted as \( r \). This resistance arises from the materials and chemical processes inside the cell that oppose the flow of current.
### Circuit Behavior
When the cell is connected to an external circuit and a current \( I \) is drawn from it:
1. **Voltage Drop Across Internal Resistance:**
- As current flows through the cell, it encounters the internal resistance. This resistance causes a voltage drop given by Ohm’s law: \( V_{\text{drop}} = I \times r \).
2. **Potential Difference Across Terminals:**
- The actual potential difference \( V \) across the terminals of the cell is the EMF minus the voltage drop due to the internal resistance. Mathematically, this is expressed as:
\[
V = \text{EMF} - I \times r
\]
- Therefore, the potential difference across the terminals is less than the EMF by the amount of voltage dropped across the internal resistance.
### Example Calculation
Consider a cell with an EMF of 12 V and an internal resistance of 1 Ω. If a current of 2 A is drawn from the cell, the voltage drop across the internal resistance is:
\[
V_{\text{drop}} = I \times r = 2 \, \text{A} \times 1 \, \Omega = 2 \, \text{V}
\]
The potential difference across the terminals will then be:
\[
V = \text{EMF} - V_{\text{drop}} = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V}
\]
### Summary
The potential difference across the terminals of a cell is less than its EMF when a current is drawn due to the internal resistance of the cell causing a voltage drop. This means that while the EMF represents the maximum potential difference when no current is flowing, the actual terminal voltage under load is reduced by the internal resistance.
### EMF and Internal Resistance
1. **EMF of a Cell:**
- The EMF of a cell is the maximum potential difference between its terminals when no current is flowing. It represents the work done per unit charge by the cell in moving the charge from one terminal to the other inside the cell.
2. **Internal Resistance:**
- Inside the cell, there is an internal resistance denoted as \( r \). This resistance arises from the materials and chemical processes inside the cell that oppose the flow of current.
### Circuit Behavior
When the cell is connected to an external circuit and a current \( I \) is drawn from it:
1. **Voltage Drop Across Internal Resistance:**
- As current flows through the cell, it encounters the internal resistance. This resistance causes a voltage drop given by Ohm’s law: \( V_{\text{drop}} = I \times r \).
2. **Potential Difference Across Terminals:**
- The actual potential difference \( V \) across the terminals of the cell is the EMF minus the voltage drop due to the internal resistance. Mathematically, this is expressed as:
\[
V = \text{EMF} - I \times r
\]
- Therefore, the potential difference across the terminals is less than the EMF by the amount of voltage dropped across the internal resistance.
### Example Calculation
Consider a cell with an EMF of 12 V and an internal resistance of 1 Ω. If a current of 2 A is drawn from the cell, the voltage drop across the internal resistance is:
\[
V_{\text{drop}} = I \times r = 2 \, \text{A} \times 1 \, \Omega = 2 \, \text{V}
\]
The potential difference across the terminals will then be:
\[
V = \text{EMF} - V_{\text{drop}} = 12 \, \text{V} - 2 \, \text{V} = 10 \, \text{V}
\]
### Summary
The potential difference across the terminals of a cell is less than its EMF when a current is drawn due to the internal resistance of the cell causing a voltage drop. This means that while the EMF represents the maximum potential difference when no current is flowing, the actual terminal voltage under load is reduced by the internal resistance.