24 cells of emf `1.5 V` each having internal resistance of 1 ohm are connected to an external resistance of `1.5` ohms. To get maximum current,

Options

A. all cells are connected in series combination
B. all cells are connected in parallel combination
C. 4 cells in each row are connected in series and 6 such rows are connected in parallel
D. 6 cells in each row are connected in series and 4 such rows are connected in parallel

Answer

To solve the problem of determining the configuration of 24 cells that will yield the maximum current when connected to an external resistance of 1.5 ohms, we will analyze each of the proposed configurations step by step.

### Step 1: Understanding the Problem
We have 24 cells, each with an EMF of 1.5 V and an internal resistance of 1 ohm. We need to determine the configuration that produces the maximum current when connected to an external resistance of 1.5 ohms.

### Step 2: Configuration A - All Cells in Series
1. **Calculate the Equivalent EMF (E_eq)**:
\[ E_{eq} = n \cdot e = 24 \cdot 1.5 = 36 \text{ V} \]

2. **Calculate the Equivalent Internal Resistance (R_eq)**:
\[ R_{eq} = n \cdot r = 24 \cdot 1 = 24 \text{ ohms} \]

3. **Calculate the Total Resistance (R_total)**:
\[ R_{total} = R_{eq} + R_{external} = 24 + 1.5 = 25.5 \text{ ohms} \]

4. **Calculate the Current (I)**:
\[ I = \frac{E_{eq}}{R_{total}} = \frac{36}{25.5} \approx 1.41 \text{ A} \]

### Step 3: Configuration B - All Cells in Parallel
1. **Calculate the Equivalent EMF (E_eq)**:
\[ E_{eq} = e = 1.5 \text{ V} \]

2. **Calculate the Equivalent Internal Resistance (R_eq)**:
\[ R_{eq} = \frac{r}{n} = \frac{1}{24} \text{ ohms} \]

3. **Calculate the Total Resistance (R_total)**:
\[ R_{total} = R_{eq} + R_{external} = \frac{1}{24} + 1.5 \approx 1.54 \text{ ohms} \]

4. **Calculate the Current (I)**:
\[ I = \frac{E_{eq}}{R_{total}} = \frac{1.5}{1.54} \approx 0.97 \text{ A} \]

### Step 4: Configuration C - 4 Cells in Series, 6 Rows in Parallel
1. **Calculate the Equivalent EMF for each row (E_eq)**:
\[ E_{eq} = 4 \cdot 1.5 = 6 \text{ V} \]

2. **Calculate the Equivalent Internal Resistance for each row (R_eq)**:
\[ R_{eq} = 4 \cdot 1 = 4 \text{ ohms} \]

3. **Calculate the Total Equivalent Resistance (R_total)**:
\[ R_{eq\_total} = \frac{R_{eq}}{n} = \frac{4}{6} = \frac{2}{3} \text{ ohms} \]
\[ R_{total} = R_{eq\_total} + R_{external} = \frac{2}{3} + 1.5 = \frac{2}{3} + \frac{9}{6} = \frac{11}{6} \text{ ohms} \]

4. **Calculate the Current (I)**:
\[ I = \frac{E_{eq}}{R_{total}} = \frac{6}{\frac{11}{6}} = \frac{36}{11} \approx 3.27 \text{ A} \]

### Step 5: Configuration D - 6 Cells in Series, 4 Rows in Parallel
1. **Calculate the Equivalent EMF for each row (E_eq)**:
\[ E_{eq} = 6 \cdot 1.5 = 9 \text{ V} \]

2. **Calculate the Equivalent Internal Resistance for each row (R_eq)**:
\[ R_{eq} = 6 \cdot 1 = 6 \text{ ohms} \]

3. **Calculate the Total Equivalent Resistance (R_total)**:
\[ R_{eq\_total} = \frac{R_{eq}}{n} = \frac{6}{4} = 1.5 \text{ ohms} \]
\[ R_{total} = R_{eq\_total} + R_{external} = 1.5 + 1.5 = 3 \text{ ohms} \]

4. **Calculate the Current (I)**:
\[ I = \frac{E_{eq}}{R_{total}} = \frac{9}{3} = 3 \text{ A} \]

### Conclusion
After calculating the current for each configuration:
- Configuration A: 1.41 A
- Configuration B: 0.97 A
- Configuration C: 3.27 A
- Configuration D: 3 A

The maximum current is obtained in **Configuration C** (4 cells in series, 6 rows in parallel) with a current of approximately **3.27 A**.