Choose the incorrect statement from the following

Options

A. The terminal voltage of a cell is greater than the emf of the cell during charging of the cell.
B. The emf of a cell is always greater than its terminal voltage.
C. The emf of a cell is greater than the terminal voltage of the cell in case of discharging of the cell.
D. None of the above.

Answer

To solve the question of identifying the incorrect statement regarding the terminal voltage and EMF of a cell, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding EMF and Terminal Voltage**:
- The EMF (Electromotive Force) of a cell is the maximum potential difference when no current flows (open circuit).
- The terminal voltage is the potential difference across the terminals of the cell when it is connected in a circuit and current flows.

2. **Charging Condition**:
- When a cell is being charged, the current flows into the cell.
- The relationship can be expressed as:
\[ V_{A} - V_{B} = E + I \cdot r \]
- Here, \(V_A\) is the potential at point A, \(V_B\) is the potential at point B, \(E\) is the EMF, \(I\) is the current, and \(r\) is the internal resistance.
- Thus, the terminal voltage during charging is:
\[ V_{terminal} = E + I \cdot r \]
- This indicates that the terminal voltage is greater than the EMF when charging.

3. **Discharging Condition**:
- When a cell is discharging, the current flows out of the cell.
- The relationship can be expressed as:
\[ V_{A} - V_{B} = E - I \cdot r \]
- Therefore, the terminal voltage during discharging is:
\[ V_{terminal} = E - I \cdot r \]
- This indicates that the terminal voltage is less than the EMF when discharging.

4. **Analyzing the Statements**:
- **Statement 1**: "The terminal voltage of a cell is greater than the EMF of the cell during the charging of the cell."
- This statement is **correct** as derived above.
- **Statement 2**: "The EMF of the cell is always greater than its terminal voltage."
- This statement is **incorrect** because during charging, the terminal voltage can be greater than the EMF.
- **Statement 3**: "The EMF of the cell is greater than the terminal voltage of the cell in case of discharging."
- This statement is **correct** as derived above.

5. **Conclusion**:
- The incorrect statement among the options provided is the second statement: "The EMF of the cell is always greater than its terminal voltage."

### Final Answer:
The incorrect statement is: **"The EMF of the cell is always greater than its terminal voltage."**