N identical calls are cannected to from a battery. When the terminals of the battery are joined directly. When the terminals of the battery are joined directly (short - ciruited), current I flows in the circuit. To obtain the maximum value of I,

Options

A. all the cells should be joined in series
B. all the cells should be joined in parallel
C. two rows fo N //2 cells each should be joined in parallel
D. `sqrtN` rows of `sqrtN` cells each should be joined in parlallel, given that `sqrtN` is an interger

Explanation

To solve the problem of how to connect N identical cells to obtain the maximum current \( I \) when the terminals of the battery are short-circuited, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Parameters**:
- Let the electromotive force (emf) of each cell be \( \epsilon \).
- Let the internal resistance of each cell be \( r \).
- There are \( N \) identical cells.

2. **Connection in Series**:
- When the cells are connected in series, the total emf \( E \) of the battery is the sum of the individual emfs:
\[ E = N \epsilon \]
- The total internal resistance \( R \) in series is the sum of the internal resistances:
\[ R = N r \]
- The current \( I_s \) flowing through the circuit when connected in series can be calculated using Ohm's law:
\[ I_s = \frac{E}{R} = \frac{N \epsilon}{N r} = \frac{\epsilon}{r} \]

3. **Connection in Parallel**:
- When the cells are connected in parallel, the total emf remains the same as that of a single cell:
\[ E = \epsilon \]
- The total internal resistance \( R \) when \( N \) cells are connected in parallel is given by:
\[ R = \frac{r}{N} \]
- The current \( I_p \) flowing through the circuit when connected in parallel can be calculated as:
\[ I_p = \frac{E}{R} = \frac{\epsilon}{\frac{r}{N}} = \frac{N \epsilon}{r} \]

4. **Comparison of Currents**:
- From the calculations:
- Current in series: \( I_s = \frac{\epsilon}{r} \)
- Current in parallel: \( I_p = \frac{N \epsilon}{r} \)
- Clearly, \( I_p > I_s \) for \( N > 1 \).

5. **Conclusion**:
- To obtain the maximum value of current \( I \), all \( N \) identical cells should be connected in parallel.

### Final Answer:
The maximum current \( I \) is obtained when all cells are connected in parallel.

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