Two conductors A and B resistance `5 omega and 10 omega` respectively are first joined in parallel and then in series. In each case the voltage applied is 20 V.
In which arrangment will the current through A and b be the same ?

Options

A. Series arrangment
B. Parallel arrangement
C. Both of the above
D. None of the above

Explanation

To determine in which arrangement the current through conductors A and B will be the same, we need to analyze both the parallel and series configurations.

### Step 1: Analyze the Parallel Arrangement
1. **Resistance Values**:
- Resistance of conductor A, \( R_A = 5 \, \Omega \)
- Resistance of conductor B, \( R_B = 10 \, \Omega \)

2. **Voltage Applied**:
- \( V = 20 \, V \)

3. **Current Calculation**:
- In a parallel circuit, the voltage across each resistor is the same. Therefore, the current through each resistor can be calculated using Ohm's Law:
\[ I_A = \frac{V}{R_A} = \frac{20 \, V}{5 \, \Omega} = 4 \, A \]
\[ I_B = \frac{V}{R_B} = \frac{20 \, V}{10 \, \Omega} = 2 \, A \]

4. **Conclusion for Parallel Arrangement**:
- The currents through A and B are different: \( I_A = 4 \, A \) and \( I_B = 2 \, A \).

### Step 2: Analyze the Series Arrangement
1. **Total Resistance in Series**:
- The total resistance \( R_{total} \) in series is the sum of the individual resistances:
\[ R_{total} = R_A + R_B = 5 \, \Omega + 10 \, \Omega = 15 \, \Omega \]

2. **Current Calculation**:
- In a series circuit, the same current flows through all components. The total current \( I \) can be calculated using Ohm's Law:
\[ I = \frac{V}{R_{total}} = \frac{20 \, V}{15 \, \Omega} = \frac{4}{3} \, A \approx 1.33 \, A \]

3. **Conclusion for Series Arrangement**:
- The current through both A and B is the same in the series arrangement, and it is approximately \( 1.33 \, A \).

### Final Conclusion
- The current through conductors A and B will be the same in the **series arrangement**.

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