Two identical conductors maintained at same temperatures are given potential differences in the ratio 1:2. Then the ratio of their drift velocities is-

Options

A. `1:2`
B. `3:2`
C. `1:1`
D. `1:2^(1//2)`

Explanation

To solve the problem, we need to find the ratio of the drift velocities of two identical conductors given that they have potential differences in the ratio of 1:2.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We have two identical conductors maintained at the same temperature.
- The potential differences across them are in the ratio \( V_1 : V_2 = 1 : 2 \).
- This implies that \( V_1 = k \) and \( V_2 = 2k \) for some constant \( k \).

**Hint**: Identify the variables and their relationships based on the problem statement.

2. **Using the Formula for Current**:
- The current \( I \) in a conductor can be expressed using the formula:
\[ I = n \cdot A \cdot e \cdot v_d \]
where:
- \( n \) = number of charge carriers per unit volume,
- \( A \) = cross-sectional area,
- \( e \) = charge of an electron,
- \( v_d \) = drift velocity.

**Hint**: Recall the formula for current and the variables involved.

3. **Relating Current and Potential Difference**:
- According to Ohm's Law, the current can also be expressed as:
\[ I = \frac{V}{R} \]
- For identical conductors, the resistance \( R \) is the same for both conductors, so we can express the currents for both conductors as:
\[ I_1 = \frac{V_1}{R} \quad \text{and} \quad I_2 = \frac{V_2}{R} \]

**Hint**: Use Ohm's Law to relate current to potential difference.

4. **Setting Up the Ratios**:
- From the current expressions:
\[ I_1 = n \cdot A \cdot e \cdot v_{d1} \quad \text{and} \quad I_2 = n \cdot A \cdot e \cdot v_{d2} \]
- Therefore, we can write:
\[ n \cdot A \cdot e \cdot v_{d1} = \frac{V_1}{R} \quad \text{and} \quad n \cdot A \cdot e \cdot v_{d2} = \frac{V_2}{R} \]

**Hint**: Relate the drift velocities to the currents.

5. **Finding the Ratio of Drift Velocities**:
- Dividing the two equations gives:
\[ \frac{n \cdot A \cdot e \cdot v_{d1}}{n \cdot A \cdot e \cdot v_{d2}} = \frac{V_1}{V_2} \]
- This simplifies to:
\[ \frac{v_{d1}}{v_{d2}} = \frac{V_1}{V_2} \]
- Substituting the values of \( V_1 \) and \( V_2 \):
\[ \frac{v_{d1}}{v_{d2}} = \frac{1}{2} \]

**Hint**: Use the relationship established to find the ratio of drift velocities.

6. **Conclusion**:
- Therefore, the ratio of their drift velocities is:
\[ \frac{v_{d1}}{v_{d2}} = \frac{1}{2} \]

### Final Answer:
The ratio of the drift velocities \( v_{d1} : v_{d2} = 1 : 2 \).