To draw the maximum current from a combination of cells, how should be the cells be grounded ?

Options

A. Parallel
B. Series
C. Depends upon the relative values of internal and external resistance
D. Mixed grouping

Answer

To determine how to draw the maximum current from a combination of cells, we need to analyze the configurations of the cells: series and parallel.

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- Cells can be connected in two main configurations: series and parallel.
- In a series configuration, the total EMF (Electromotive Force) is the sum of the individual EMFs, while the total internal resistance is the sum of the individual internal resistances.
- In a parallel configuration, the total EMF remains the same as that of one cell, but the total internal resistance decreases.

2. **Current in Series Configuration**:
- For n cells connected in series, each with an EMF \(E\) and internal resistance \(r\):
\[ \text{Total EMF} = nE \]
\[ \text{Total Internal Resistance} = nr \]
- The total resistance in the circuit (including external resistance \(R\)) is:
\[ R_{\text{total}} = nr + R \]
- Using Ohm's law, the current \(I\) can be expressed as:
\[ I = \frac{V}{R_{\text{total}}} = \frac{nE}{nr + R} \]

3. **Current in Parallel Configuration**:
- For n cells connected in parallel, the total EMF remains \(E\), and the total internal resistance \(r_{\text{total}}\) is given by:
\[ \frac{1}{r_{\text{total}}} = \frac{1}{r} + \frac{1}{r} + ... + \frac{1}{r} = \frac{n}{r} \implies r_{\text{total}} = \frac{r}{n} \]
- The total resistance in the circuit is:
\[ R_{\text{total}} = \frac{r}{n} + R \]
- The current \(I\) in this case is:
\[ I = \frac{nE}{\frac{r}{n} + R} \]

4. **Comparing Currents**:
- To find out which configuration provides maximum current, we need to compare the expressions for current in both configurations.
- For maximum current, we need to analyze the conditions:
- If \(R + nr < \frac{r}{n} + R\), then the cells should be connected in parallel.
- Conversely, if \(R + nr > \frac{r}{n} + R\), then the cells should be connected in series.

5. **Conclusion**:
- The configuration that yields maximum current depends on the relative values of the internal resistance of the cells and the external resistance.
- If the internal resistance is significantly lower than the external resistance, connecting the cells in parallel will yield a higher current. If the internal resistance is higher, connecting them in series will yield a higher current.

### Final Answer:
To draw the maximum current from a combination of cells, the cells should be connected in parallel if the internal resistance is low compared to the external resistance. Conversely, if the internal resistance is high, they should be connected in series.