Why is the terminal voltage of a cell less than emf?
2 Answers
The terminal voltage of a cell is often less than its electromotive force (emf) due to several factors related to internal resistance and the state of the cell. Here’s a detailed breakdown of the concepts involved:
### 1. Understanding emf and Terminal Voltage
- **Electromotive Force (emf)**: This is the maximum potential difference between the terminals of a cell when no current is flowing. It represents the energy provided per unit charge by the cell’s chemical reactions.
- **Terminal Voltage (V)**: This is the actual voltage output of the cell when it is connected to a circuit and current is flowing. It can be measured directly across the terminals of the cell.
### 2. Internal Resistance
- Every real battery or cell has some internal resistance (denoted as \( r \)). This resistance is due to the materials and chemical processes within the cell. When current flows through the cell, this internal resistance causes a voltage drop within the cell itself.
### 3. Voltage Drop in the Cell
- When a current \( I \) flows out of the cell, the voltage drop across the internal resistance can be calculated using Ohm's Law:
\[
\text{Voltage drop} = I \times r
\]
- As a result, the terminal voltage \( V \) can be expressed as:
\[
V = \text{emf} - I \times r
\]
### 4. Factors Affecting Terminal Voltage
- **Load on the Cell**: The amount of current drawn from the cell affects the terminal voltage. Higher current results in a greater voltage drop due to internal resistance, leading to a lower terminal voltage.
- **State of Charge**: A partially discharged cell may have higher internal resistance than a fully charged one, resulting in a lower terminal voltage during discharge.
- **Temperature**: Changes in temperature can affect both the internal resistance and the chemical reactions within the cell, thereby impacting the terminal voltage.
### 5. Practical Implications
In practical scenarios, this difference between terminal voltage and emf is significant:
- **Power Delivery**: The lower terminal voltage under load means that the actual power delivered to a device is less than what might be expected based solely on the emf of the cell.
- **Battery Performance**: Understanding this difference helps in designing circuits and systems that can effectively manage battery usage, especially in applications like electric vehicles, where maintaining performance under load is crucial.
### Summary
In summary, the terminal voltage of a cell is less than its emf primarily due to the internal resistance of the cell, which causes a voltage drop when current flows. This difference is influenced by the current being drawn, the state of charge of the cell, and external conditions like temperature. Understanding these concepts is essential for effectively utilizing batteries in various applications.
### 1. Understanding emf and Terminal Voltage
- **Electromotive Force (emf)**: This is the maximum potential difference between the terminals of a cell when no current is flowing. It represents the energy provided per unit charge by the cell’s chemical reactions.
- **Terminal Voltage (V)**: This is the actual voltage output of the cell when it is connected to a circuit and current is flowing. It can be measured directly across the terminals of the cell.
### 2. Internal Resistance
- Every real battery or cell has some internal resistance (denoted as \( r \)). This resistance is due to the materials and chemical processes within the cell. When current flows through the cell, this internal resistance causes a voltage drop within the cell itself.
### 3. Voltage Drop in the Cell
- When a current \( I \) flows out of the cell, the voltage drop across the internal resistance can be calculated using Ohm's Law:
\[
\text{Voltage drop} = I \times r
\]
- As a result, the terminal voltage \( V \) can be expressed as:
\[
V = \text{emf} - I \times r
\]
### 4. Factors Affecting Terminal Voltage
- **Load on the Cell**: The amount of current drawn from the cell affects the terminal voltage. Higher current results in a greater voltage drop due to internal resistance, leading to a lower terminal voltage.
- **State of Charge**: A partially discharged cell may have higher internal resistance than a fully charged one, resulting in a lower terminal voltage during discharge.
- **Temperature**: Changes in temperature can affect both the internal resistance and the chemical reactions within the cell, thereby impacting the terminal voltage.
### 5. Practical Implications
In practical scenarios, this difference between terminal voltage and emf is significant:
- **Power Delivery**: The lower terminal voltage under load means that the actual power delivered to a device is less than what might be expected based solely on the emf of the cell.
- **Battery Performance**: Understanding this difference helps in designing circuits and systems that can effectively manage battery usage, especially in applications like electric vehicles, where maintaining performance under load is crucial.
### Summary
In summary, the terminal voltage of a cell is less than its emf primarily due to the internal resistance of the cell, which causes a voltage drop when current flows. This difference is influenced by the current being drawn, the state of charge of the cell, and external conditions like temperature. Understanding these concepts is essential for effectively utilizing batteries in various applications.
The terminal voltage of a cell or battery is typically less than its electromotive force (EMF) due to the internal resistance of the cell. To understand why this is the case, let’s break down the concepts and the process in detail:
### 1. **Definitions**
- **EMF (Electromotive Force):** This is the maximum potential difference a cell can provide when no current is flowing through the circuit. It represents the energy supplied per unit charge by the cell's internal chemical processes.
- **Terminal Voltage:** This is the actual voltage output of the cell when a current is flowing through the circuit. It’s the potential difference measured across the cell's terminals.
### 2. **Internal Resistance**
Cells and batteries are not perfect; they have an internal resistance, denoted as \( r_{\text{int}} \). This resistance arises due to the materials and construction of the cell, including the electrolyte, electrodes, and connectors. When a current flows through the cell, this internal resistance causes a voltage drop within the cell itself.
### 3. **Current Flow and Voltage Drop**
When a cell is connected to a circuit and current \( I \) flows through it, the voltage drop across the internal resistance can be calculated using Ohm's Law:
\[ V_{\text{drop}} = I \cdot r_{\text{int}} \]
Here’s how it affects the terminal voltage:
- **EMF (E):** This is the voltage generated by the cell when there’s no load connected, so there’s no current flowing through the internal resistance. Hence, EMF is the maximum potential difference.
- **Terminal Voltage (V):** When a load is connected and current flows, the terminal voltage is less than the EMF because the internal resistance causes a voltage drop.
So, the terminal voltage can be expressed as:
\[ V = E - I \cdot r_{\text{int}} \]
where:
- \( V \) is the terminal voltage,
- \( E \) is the EMF,
- \( I \) is the current flowing through the circuit,
- \( r_{\text{int}} \) is the internal resistance.
### 4. **Why Is the Terminal Voltage Less?**
The terminal voltage is less than the EMF because the internal resistance causes a voltage drop proportional to the current flowing through the cell. The greater the current, the larger the voltage drop due to internal resistance, leading to a more significant difference between the EMF and the terminal voltage.
### 5. **Practical Implications**
In practical applications:
- **Low Current Loads:** When the current is low, the voltage drop across the internal resistance is minimal, and the terminal voltage is closer to the EMF.
- **High Current Loads:** With high currents, the internal resistance causes a more significant voltage drop, reducing the terminal voltage substantially.
This phenomenon is why batteries and cells are rated with their EMF, and their performance can be affected by internal resistance, especially under different load conditions.
### 1. **Definitions**
- **EMF (Electromotive Force):** This is the maximum potential difference a cell can provide when no current is flowing through the circuit. It represents the energy supplied per unit charge by the cell's internal chemical processes.
- **Terminal Voltage:** This is the actual voltage output of the cell when a current is flowing through the circuit. It’s the potential difference measured across the cell's terminals.
### 2. **Internal Resistance**
Cells and batteries are not perfect; they have an internal resistance, denoted as \( r_{\text{int}} \). This resistance arises due to the materials and construction of the cell, including the electrolyte, electrodes, and connectors. When a current flows through the cell, this internal resistance causes a voltage drop within the cell itself.
### 3. **Current Flow and Voltage Drop**
When a cell is connected to a circuit and current \( I \) flows through it, the voltage drop across the internal resistance can be calculated using Ohm's Law:
\[ V_{\text{drop}} = I \cdot r_{\text{int}} \]
Here’s how it affects the terminal voltage:
- **EMF (E):** This is the voltage generated by the cell when there’s no load connected, so there’s no current flowing through the internal resistance. Hence, EMF is the maximum potential difference.
- **Terminal Voltage (V):** When a load is connected and current flows, the terminal voltage is less than the EMF because the internal resistance causes a voltage drop.
So, the terminal voltage can be expressed as:
\[ V = E - I \cdot r_{\text{int}} \]
where:
- \( V \) is the terminal voltage,
- \( E \) is the EMF,
- \( I \) is the current flowing through the circuit,
- \( r_{\text{int}} \) is the internal resistance.
### 4. **Why Is the Terminal Voltage Less?**
The terminal voltage is less than the EMF because the internal resistance causes a voltage drop proportional to the current flowing through the cell. The greater the current, the larger the voltage drop due to internal resistance, leading to a more significant difference between the EMF and the terminal voltage.
### 5. **Practical Implications**
In practical applications:
- **Low Current Loads:** When the current is low, the voltage drop across the internal resistance is minimal, and the terminal voltage is closer to the EMF.
- **High Current Loads:** With high currents, the internal resistance causes a more significant voltage drop, reducing the terminal voltage substantially.
This phenomenon is why batteries and cells are rated with their EMF, and their performance can be affected by internal resistance, especially under different load conditions.