Why terminal potential difference is less than the emf of a cell?
2 Answers
The terminal potential difference of a cell is often less than its electromotive force (emf) due to internal resistance. When a current flows through the cell, some energy is lost within the cell itself as heat due to this internal resistance. This leads to a drop in potential across the internal resistance, resulting in a lower terminal voltage than the emf.
The relationship can be expressed by the equation:
\[
V = \text{emf} - I \cdot r_{\text{internal}}
\]
where:
- \( V \) is the terminal potential difference,
- \( \text{emf} \) is the electromotive force of the cell,
- \( I \) is the current flowing through the circuit,
- \( r_{\text{internal}} \) is the internal resistance of the cell.
So, when there is current flow, the terminal voltage is reduced because of the voltage drop across the internal resistance.
The relationship can be expressed by the equation:
\[
V = \text{emf} - I \cdot r_{\text{internal}}
\]
where:
- \( V \) is the terminal potential difference,
- \( \text{emf} \) is the electromotive force of the cell,
- \( I \) is the current flowing through the circuit,
- \( r_{\text{internal}} \) is the internal resistance of the cell.
So, when there is current flow, the terminal voltage is reduced because of the voltage drop across the internal resistance.
The terminal potential difference (V) of a cell is generally less than its electromotive force (EMF, \( \mathcal{E} \)) due to the internal resistance of the cell. To understand this concept thoroughly, let’s break it down step by step:
### 1. **EMF of a Cell**
The EMF of a cell, denoted by \( \mathcal{E} \), is the maximum potential difference between the cell's terminals when no current is flowing (i.e., in an open-circuit condition). It represents the total electrical energy provided per coulomb of charge by the cell.
### 2. **Internal Resistance**
Every real cell or battery has some internal resistance (r), which is the resistance offered by the materials inside the cell to the flow of current. This internal resistance causes a voltage drop inside the cell when current flows.
### 3. **Terminal Potential Difference**
When the cell is connected in a circuit and current (I) flows, the terminal potential difference (V) across the cell is affected by the internal resistance. The relationship between EMF, terminal potential difference, current, and internal resistance can be described by the following equation:
\[ V = \mathcal{E} - I \cdot r \]
where:
- \( V \) is the terminal potential difference,
- \( \mathcal{E} \) is the EMF of the cell,
- \( I \) is the current flowing through the cell,
- \( r \) is the internal resistance of the cell.
### 4. **Why Terminal Potential Difference is Less**
When current flows through the cell, a part of the EMF is used to overcome the internal resistance. This causes a drop in voltage inside the cell. The terminal potential difference you measure is therefore less than the EMF by an amount equal to the voltage drop across the internal resistance, which is \( I \cdot r \).
### 5. **Example to Illustrate**
Consider a cell with an EMF of 12V and an internal resistance of 1 ohm. Suppose a current of 2A is flowing through the cell. The voltage drop due to the internal resistance can be calculated as:
\[ \text{Voltage drop} = I \cdot r = 2 \text{A} \times 1 \text{ohm} = 2 \text{V} \]
So, the terminal potential difference is:
\[ V = \mathcal{E} - I \cdot r = 12 \text{V} - 2 \text{V} = 10 \text{V} \]
Thus, the terminal potential difference (10V) is less than the EMF (12V) by the amount of the internal voltage drop.
### 6. **Conclusion**
The key reason why the terminal potential difference is less than the EMF of a cell is due to the internal resistance that causes a voltage drop when current flows. This difference becomes more pronounced with higher currents and larger internal resistances.
### 1. **EMF of a Cell**
The EMF of a cell, denoted by \( \mathcal{E} \), is the maximum potential difference between the cell's terminals when no current is flowing (i.e., in an open-circuit condition). It represents the total electrical energy provided per coulomb of charge by the cell.
### 2. **Internal Resistance**
Every real cell or battery has some internal resistance (r), which is the resistance offered by the materials inside the cell to the flow of current. This internal resistance causes a voltage drop inside the cell when current flows.
### 3. **Terminal Potential Difference**
When the cell is connected in a circuit and current (I) flows, the terminal potential difference (V) across the cell is affected by the internal resistance. The relationship between EMF, terminal potential difference, current, and internal resistance can be described by the following equation:
\[ V = \mathcal{E} - I \cdot r \]
where:
- \( V \) is the terminal potential difference,
- \( \mathcal{E} \) is the EMF of the cell,
- \( I \) is the current flowing through the cell,
- \( r \) is the internal resistance of the cell.
### 4. **Why Terminal Potential Difference is Less**
When current flows through the cell, a part of the EMF is used to overcome the internal resistance. This causes a drop in voltage inside the cell. The terminal potential difference you measure is therefore less than the EMF by an amount equal to the voltage drop across the internal resistance, which is \( I \cdot r \).
### 5. **Example to Illustrate**
Consider a cell with an EMF of 12V and an internal resistance of 1 ohm. Suppose a current of 2A is flowing through the cell. The voltage drop due to the internal resistance can be calculated as:
\[ \text{Voltage drop} = I \cdot r = 2 \text{A} \times 1 \text{ohm} = 2 \text{V} \]
So, the terminal potential difference is:
\[ V = \mathcal{E} - I \cdot r = 12 \text{V} - 2 \text{V} = 10 \text{V} \]
Thus, the terminal potential difference (10V) is less than the EMF (12V) by the amount of the internal voltage drop.
### 6. **Conclusion**
The key reason why the terminal potential difference is less than the EMF of a cell is due to the internal resistance that causes a voltage drop when current flows. This difference becomes more pronounced with higher currents and larger internal resistances.