Two resistors of resistances `2 Omega and 4 Omega` when connected to a battery will have :

Options

A. same current flowing through them when connected in parallel
B. same current flowing through then when connected is series
C. same potential difference across them when connected is series
D. different potential difference across them when connected in parallel

Explanation

To solve the question regarding the behavior of two resistors of resistances \(2 \, \Omega\) and \(4 \, \Omega\) when connected to a battery, we will analyze the two configurations: series and parallel.

### Step-by-Step Solution:

1. **Understanding Series Connection**:
- In a series connection, the same current flows through all components. Therefore, if we connect the \(2 \, \Omega\) and \(4 \, \Omega\) resistors in series, the current \(I\) through both resistors will be the same.
- **Formula**: \(I = \frac{V}{R_{total}}\), where \(R_{total} = R_1 + R_2 = 2 \, \Omega + 4 \, \Omega = 6 \, \Omega\).

2. **Understanding Parallel Connection**:
- In a parallel connection, the potential difference (voltage) across each resistor is the same, but the current through each resistor can be different.
- The total current \(I\) from the battery is divided between the two resistors. The current through each resistor can be calculated using Ohm's Law: \(I = \frac{V}{R}\).
- For the \(2 \, \Omega\) resistor, \(I_1 = \frac{V}{2}\) and for the \(4 \, \Omega\) resistor, \(I_2 = \frac{V}{4}\).

3. **Evaluating the Options**:
- **Option 1**: "Same current flowing through them when connected in parallel" - This is incorrect because in parallel, the current is divided.
- **Option 2**: "Same current flowing through them when connected in series" - This is correct because in series, the current is the same through both resistors.
- **Option 3**: "Same potential difference across them when connected in series" - This is incorrect because the potential difference across each resistor is different (2I and 4I).
- **Option 4**: "Different potential differences across them when connected in parallel" - This is incorrect because the potential difference across each resistor is the same in parallel.

4. **Conclusion**:
- The only correct statement is **Option 2**: "Same current flowing through them when connected in series".