Two conductors made of the same material have lengths `L` and `2L` but have equal resistance. The two are connected in series in a circuit which current is flowing. Which of the following is/are correct?

Options

A. The potential difference across the two conductors is the same
B. the drift speed is larger inte conductor of lengthL
C. The electric field in the first conductor is twice that in the second
D. the electric field in the second conductor is twice that in the first

Explanation

To solve the problem, we need to analyze the given information about two conductors made of the same material, with lengths \( L \) and \( 2L \), which have equal resistance. We will derive the relationships between their areas, current, drift velocity, and electric field.

### Step-by-step Solution:

1. **Understanding Resistance**:
The resistance \( R \) of a conductor is given by the formula:
\[ R = \frac{\rho L}{A} \]
where \( \rho \) is the resistivity of the material, \( L \) is the length of the conductor, and \( A \) is the cross-sectional area.

2. **Setting Up the Equations**:
For the two conductors:
- For conductor 1 (length \( L \)):
\[ R_1 = \frac{\rho L}{A_1} \]
- For conductor 2 (length \( 2L \)):
\[ R_2 = \frac{\rho (2L)}{A_2} \]

Given that \( R_1 = R_2 \), we can equate the two expressions:
\[ \frac{\rho L}{A_1} = \frac{\rho (2L)}{A_2} \]

3. **Cancelling Common Terms**:
Since \( \rho \) and \( L \) are common in both equations, we can cancel them out:
\[ \frac{1}{A_1} = \frac{2}{A_2} \]
Rearranging gives:
\[ A_2 = 2A_1 \]

4. **Current in Series**:
When the two conductors are connected in series, the current \( I \) flowing through both conductors is the same.

5. **Potential Drop Across Each Conductor**:
The potential drop across each conductor can be expressed as:
- For conductor 1:
\[ V_1 = I R_1 \]
- For conductor 2:
\[ V_2 = I R_2 \]
Since \( R_1 = R_2 \), it follows that:
\[ V_1 = V_2 \]
Therefore, the potential difference across both conductors is the same.

6. **Drift Velocity**:
The current can also be expressed in terms of drift velocity \( v_d \):
\[ I = n e v_d A \]
where \( n \) is the number of charge carriers per unit volume and \( e \) is the charge of an electron. Since the current is the same in both conductors:
\[ v_{d1} A_1 = v_{d2} A_2 \]
Substituting \( A_2 = 2A_1 \):
\[ v_{d1} A_1 = v_{d2} (2A_1) \]
Simplifying gives:
\[ v_{d1} = 2 v_{d2} \]
Thus, the drift velocity in conductor 1 (length \( L \)) is greater than in conductor 2 (length \( 2L \)).

7. **Electric Field**:
The electric field \( E \) in a conductor is given by:
\[ E = \frac{V}{L} \]
Since \( V_1 = V_2 \) and the lengths are different, we can express:
\[ E_1 = \frac{V_1}{L}, \quad E_2 = \frac{V_2}{2L} \]
Since \( V_1 = V_2 \):
\[ E_1 = 2E_2 \]
Thus, the electric field in conductor 1 is greater than in conductor 2.

### Conclusion:
- The potential difference across both conductors is the same.
- The drift velocity is larger in the conductor of length \( L \).
- The electric field in the first conductor is twice that of the second conductor.