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 combination will the voltage across the conductors 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 solve the problem, we need to analyze the two configurations of the resistors A and B: first in parallel and then in series.

### Step 1: Understand the configurations

1. **Parallel Configuration**: In a parallel connection, the voltage across each component is the same. Therefore, if we connect resistors A (5 ohm) and B (10 ohm) in parallel and apply a voltage of 20 V, the voltage across both A and B will be 20 V.

2. **Series Configuration**: In a series connection, the same current flows through each component, but the voltage across each component can be different depending on their resistances. The total voltage is divided among the resistors based on their resistance values.

### Step 2: Calculate the voltage across each resistor in series

1. **Total Resistance in Series**:
\[ R_{total} = R_A + R_B = 5 \, \Omega + 10 \, \Omega = 15 \, \Omega \]

2. **Current through the circuit**: Using Ohm's law, we can find the current (I) flowing through the series circuit when a voltage of 20 V is applied:
\[ I = \frac{V}{R_{total}} = \frac{20 \, V}{15 \, \Omega} = \frac{4}{3} \, A \approx 1.33 \, A \]

3. **Voltage across each resistor**:
- Voltage across A (5 ohm):
\[ V_A = I \times R_A = \frac{4}{3} \, A \times 5 \, \Omega = \frac{20}{3} \, V \approx 6.67 \, V \]
- Voltage across B (10 ohm):
\[ V_B = I \times R_B = \frac{4}{3} \, A \times 10 \, \Omega = \frac{40}{3} \, V \approx 13.33 \, V \]

### Step 3: Compare the voltages

- In the **parallel configuration**, the voltage across both A and B is 20 V.
- In the **series configuration**, the voltages across A and B are approximately 6.67 V and 13.33 V respectively.

### Conclusion

The voltage across the conductors A and B will be the same in the **parallel configuration**.