Two resistors of resistance 2 ohm and 4 ohm when connected to a battery will have

Options

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

Explanation

To solve the question regarding the two resistors of resistance 2 ohm and 4 ohm when connected to a battery, we need to analyze their behavior in both series and parallel configurations.

### Step-by-Step Solution:

1. **Identify the Configuration**:
We have two resistors: R1 = 2 ohms and R2 = 4 ohms. We will analyze both series and parallel connections.

2. **Series Connection**:
- In a series connection, the total resistance (R_total) is the sum of the individual resistances.
- Formula:
\[ R_{\text{total(series)}} = R_1 + R_2 = 2 \, \Omega + 4 \, \Omega = 6 \, \Omega \]
- In a series circuit, the same current flows through both resistors.

3. **Parallel Connection**:
- In a parallel connection, the total resistance (R_total) can be calculated using the formula:
\[ \frac{1}{R_{\text{total(parallel)}}} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{2 \, \Omega} + \frac{1}{4 \, \Omega} \]
- Finding a common denominator (which is 4):
\[ \frac{1}{R_{\text{total(parallel)}}} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \]
- Thus, the total resistance in parallel is:
\[ R_{\text{total(parallel)}} = \frac{4}{3} \, \Omega \approx 1.33 \, \Omega \]
- In a parallel circuit, the potential difference (voltage) across each resistor is the same.

4. **Summary of Findings**:
- In series:
- Total resistance = 6 ohms
- Same current flows through both resistors.
- In parallel:
- Total resistance = 1.33 ohms
- Same potential difference across both resistors.

### Conclusion:
When connected to a battery:
- In series, the current is the same through both resistors, but the total resistance is 6 ohms.
- In parallel, the potential difference is the same across both resistors, but the total resistance is approximately 1.33 ohms.