Which of the following statements is/are correct?

Options

A. If n identical cells are connected in series and then the battery thus formed is short circuited by a conduction wire, current through the wire will be independent of n
B. If n identical cells are connected in parallel and then the battery thus formed is short circuited by conducting wire, the current through the wire will be proportional to n
C. If n identical cells are connected in parallel are then the battery thus formed is short circuited by a wire having a constant resistance, the current through the wire will increase as n increases
D. None of these

Answer

To determine which statements are correct regarding the behavior of identical cells connected in series and parallel, we can analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding Series Connection**:
- When n identical cells are connected in series, the total voltage (V_total) is the sum of the voltages of each cell. If each cell has a voltage V, then:
\[ V_{total} = n \cdot V \]
- If a short circuit occurs, the total resistance is very low (ideally zero), leading to a very high current. However, the current through the wire will be determined by the internal resistance of the cells and the voltage provided. Therefore, the current is not independent of n; it depends on the total voltage and the internal resistance.

**Hint**: Remember that in a series connection, voltage adds up, but the current depends on the total voltage and resistance.

2. **Understanding Parallel Connection**:
- When n identical cells are connected in parallel, the total voltage remains the same as that of one cell (V). The total current (I_total) supplied by the cells is the sum of the currents through each cell. Thus:
\[ I_{total} = n \cdot I_{cell} \]
- If a short circuit occurs, the current will increase with the number of cells because more paths for current flow are available. Hence, the current through the wire will indeed increase as n increases.

**Hint**: In a parallel connection, the voltage remains constant, but the current increases with the number of cells.

3. **Analyzing the Statements**:
- **Statement 1**: If n identical cells are connected in series and short-circuited, the current is independent of n. **(Incorrect)**
- **Statement 2**: If n identical cells are connected in parallel and short-circuited, the current increases as n increases. **(Correct)**
- **Statement 3**: The current through a short circuit is proportional to n in parallel connection. **(Correct)**
- **Statement 4**: If n identical cells are connected in series and short-circuited, the current is proportional to n. **(Incorrect)**

4. **Conclusion**:
- The correct statements are those regarding the parallel connection (Statements 2 and 3).

### Final Answer:
The correct statements are:
- Statement 2: Correct
- Statement 3: Correct
- Statement 1 and 4: Incorrect