A battery of 24 cells each of emf 1.5 V and internal resistnace `2Omega` is to be connected in order to send the maximum current through a `12Omega` resistor. The correct arrangement of cells will be

Options

A. 2 rows of 12 cells connected in parallel
B. 3rows of 8 cells connected in parallel
C. 4 rows of 6 cells connected in parallel
D. All of these

Answer

To solve the problem of connecting 24 cells, each with an emf of 1.5 V and an internal resistance of 2 Ω, to send the maximum current through a 12 Ω resistor, we can follow these steps:

### Step 1: Understand the Configuration
We have 24 cells, each with an emf of 1.5 V and an internal resistance of 2 Ω. We need to determine how to connect these cells to maximize the current through a 12 Ω resistor.

### Step 2: Define Variables
Let:
- \( n \) = number of cells in series in each row
- \( m \) = number of rows connected in parallel

### Step 3: Calculate Total Emf and Internal Resistance
When cells are connected in series:
- The total emf of one row = \( n \times 1.5 \, \text{V} \)
- The internal resistance of one row = \( n \times 2 \, \Omega \)

When rows are connected in parallel:
- The total emf remains the same as one row = \( n \times 1.5 \, \text{V} \)
- The total internal resistance of \( m \) rows = \( \frac{n \times 2}{m} \, \Omega \)

### Step 4: Apply the Condition for Maximum Current
For maximum current through the external resistor \( R \) (which is 12 Ω), the condition is:
\[ R = \frac{n}{m} \times 2 \]
Thus,
\[ 12 = \frac{n}{m} \times 2 \]
From this, we can derive:
\[ n = 6m \] (Equation 1)

### Step 5: Use the Total Number of Cells
The total number of cells is given as 24:
\[ n \times m = 24 \] (Equation 2)

### Step 6: Substitute and Solve
Substituting Equation 1 into Equation 2:
\[ 6m \times m = 24 \]
\[ 6m^2 = 24 \]
\[ m^2 = 4 \]
\[ m = 2 \]

Now substituting \( m \) back into Equation 1 to find \( n \):
\[ n = 6 \times 2 = 12 \]

### Step 7: Conclusion
Thus, we find that:
- Number of cells in series \( n = 12 \)
- Number of rows \( m = 2 \)

Therefore, the correct arrangement of cells is **2 rows of 12 cells connected in parallel**.