Which arrangement of four identical resistances should be sued to draw maximum energy from cell of voltage V

Options

A.
B.
C.
D.

Explanation

To determine which arrangement of four identical resistances will draw maximum energy from a cell of voltage V, we need to analyze the equivalent resistance of different configurations of the resistors. The power drawn from the cell is given by the formula:

\[ P = \frac{V^2}{R_{eq}} \]

Where:
- \( P \) is the power,
- \( V \) is the voltage of the cell,
- \( R_{eq} \) is the equivalent resistance of the arrangement.

To maximize power, we need to minimize the equivalent resistance \( R_{eq} \).

### Step-by-Step Solution:

1. **Identify the Configurations**:
We have four configurations to analyze:
- Option 1: Two pairs of resistors in parallel, then in series.
- Option 2: All four resistors in parallel.
- Option 3: All four resistors in series.
- Option 4: Two resistors in parallel, then in series with the other two resistors in parallel.

2. **Calculate the Equivalent Resistance for Each Option**:
- **Option 1**:
- Two resistors in parallel:
\[ R_{eq1} = \frac{R}{2} \]
- The other two resistors in parallel:
\[ R_{eq2} = \frac{R}{2} \]
- Total equivalent resistance:
\[ R_{eq} = R_{eq1} + R_{eq2} = \frac{R}{2} + \frac{R}{2} = R \]

- **Option 2**:
- All four resistors in parallel:
\[ R_{eq} = \frac{R}{4} \]

- **Option 3**:
- All four resistors in series:
\[ R_{eq} = 4R \]

- **Option 4**:
- Two resistors in parallel:
\[ R_{eq1} = \frac{R}{2} \]
- The other two resistors in parallel:
\[ R_{eq2} = \frac{R}{2} \]
- Total equivalent resistance:
\[ R_{eq} = R_{eq1} + R_{eq2} = \frac{R}{2} + \frac{R}{2} = R \]

3. **Compare the Equivalent Resistances**:
- Option 1: \( R \)
- Option 2: \( \frac{R}{4} \)
- Option 3: \( 4R \)
- Option 4: \( R \)

4. **Determine the Minimum Resistance**:
The minimum equivalent resistance is found in Option 2, where all four resistors are in parallel:
\[ R_{eq} = \frac{R}{4} \]

5. **Conclusion**:
To draw maximum energy from the cell, the arrangement of four identical resistances should be all four resistors connected in parallel (Option 2).

### Final Answer:
The arrangement of four identical resistances that should be used to draw maximum energy from a cell of voltage V is **all four resistors in parallel**.