Why is terminal potential difference always less than emf of the cell?
2 Answers
The terminal potential difference of a cell is always less than its electromotive force (emf) due to the internal resistance of the cell. When a current flows through the cell, some of the energy is lost as heat within the cell due to this internal resistance.
The relationship can be expressed with the formula:
\[
V = \text{emf} - I \cdot r
\]
where:
- \( V \) is the terminal potential difference,
- \( \text{emf} \) is the electromotive force of the cell,
- \( I \) is the current flowing through the circuit, and
- \( r \) is the internal resistance of the cell.
As a result, when the current is drawn from the cell, the terminal voltage (the voltage available to external components) decreases, reflecting this loss due to internal resistance. Hence, the terminal potential difference is always less than the emf when a current is being drawn from the cell.
The relationship can be expressed with the formula:
\[
V = \text{emf} - I \cdot r
\]
where:
- \( V \) is the terminal potential difference,
- \( \text{emf} \) is the electromotive force of the cell,
- \( I \) is the current flowing through the circuit, and
- \( r \) is the internal resistance of the cell.
As a result, when the current is drawn from the cell, the terminal voltage (the voltage available to external components) decreases, reflecting this loss due to internal resistance. Hence, the terminal potential difference is always less than the emf when a current is being drawn from the cell.
The terminal potential difference of a cell is always less than the electromotive force (EMF) of the cell due to internal resistance. Let me explain the concept in detail:
### 1. **Electromotive Force (EMF)**
- **Definition**: EMF 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 to move charges through the external circuit.
- **Formula**: EMF (E) = \( V_{oc} \), where \( V_{oc} \) is the open-circuit voltage.
### 2. **Internal Resistance**
- **Definition**: Every real cell has some internal resistance (r). This resistance arises due to the materials and construction of the cell, including the electrolyte and electrodes.
- **Effect**: When a current (I) flows through the cell, a voltage drop occurs across the internal resistance. This drop reduces the potential difference that can be measured across the cell's terminals.
### 3. **Terminal Potential Difference**
- **Definition**: The terminal potential difference (V) is the actual voltage measured across the terminals of the cell when current is flowing through the circuit.
- **Relationship with EMF**: The terminal potential difference is given by:
\[ V = E - I \cdot r \]
Where:
- \( E \) = EMF of the cell
- \( I \) = Current flowing through the circuit
- \( r \) = Internal resistance of the cell
### 4. **Reason for the Difference**
- **Current Flow and Voltage Drop**: When current flows through the cell, the internal resistance causes a voltage drop. This drop subtracts from the EMF, leading to a lower terminal potential difference.
For example, if a cell has an EMF of 1.5 V and an internal resistance of 0.5 Ω, and the current flowing through the circuit is 2 A, then the voltage drop across the internal resistance would be:
\[ I \cdot r = 2 \, \text{A} \times 0.5 \, \Omega = 1 \, \text{V} \]
Thus, the terminal potential difference \( V \) would be:
\[ V = E - I \cdot r = 1.5 \, \text{V} - 1 \, \text{V} = 0.5 \, \text{V} \]
### Summary
In essence, the terminal potential difference is always less than the EMF due to the internal resistance of the cell causing a voltage drop when current flows. The greater the current or internal resistance, the greater the difference between EMF and terminal potential difference.
### 1. **Electromotive Force (EMF)**
- **Definition**: EMF 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 to move charges through the external circuit.
- **Formula**: EMF (E) = \( V_{oc} \), where \( V_{oc} \) is the open-circuit voltage.
### 2. **Internal Resistance**
- **Definition**: Every real cell has some internal resistance (r). This resistance arises due to the materials and construction of the cell, including the electrolyte and electrodes.
- **Effect**: When a current (I) flows through the cell, a voltage drop occurs across the internal resistance. This drop reduces the potential difference that can be measured across the cell's terminals.
### 3. **Terminal Potential Difference**
- **Definition**: The terminal potential difference (V) is the actual voltage measured across the terminals of the cell when current is flowing through the circuit.
- **Relationship with EMF**: The terminal potential difference is given by:
\[ V = E - I \cdot r \]
Where:
- \( E \) = EMF of the cell
- \( I \) = Current flowing through the circuit
- \( r \) = Internal resistance of the cell
### 4. **Reason for the Difference**
- **Current Flow and Voltage Drop**: When current flows through the cell, the internal resistance causes a voltage drop. This drop subtracts from the EMF, leading to a lower terminal potential difference.
For example, if a cell has an EMF of 1.5 V and an internal resistance of 0.5 Ω, and the current flowing through the circuit is 2 A, then the voltage drop across the internal resistance would be:
\[ I \cdot r = 2 \, \text{A} \times 0.5 \, \Omega = 1 \, \text{V} \]
Thus, the terminal potential difference \( V \) would be:
\[ V = E - I \cdot r = 1.5 \, \text{V} - 1 \, \text{V} = 0.5 \, \text{V} \]
### Summary
In essence, the terminal potential difference is always less than the EMF due to the internal resistance of the cell causing a voltage drop when current flows. The greater the current or internal resistance, the greater the difference between EMF and terminal potential difference.