Two wires each of radius of cross section `r` but of different materials are connected together end to end (in series). If the densities of charge carries in the two wires are in the ratio `1:4`, the drift velocity of electrons in the two wires will be in the ratio:

Options

A. `1:2`
B. `2:1`
C. `4:1`
D. `1:4`

Answer

To solve the problem, we need to find the ratio of the drift velocities of electrons in two wires connected in series, given that the densities of charge carriers in the two wires are in the ratio of 1:4.

### Step-by-Step Solution:

1. **Define Variables**:
- Let \( n_1 \) be the density of charge carriers in the first wire.
- Let \( n_2 \) be the density of charge carriers in the second wire.
- Let \( v_{d1} \) be the drift velocity of electrons in the first wire.
- Let \( v_{d2} \) be the drift velocity of electrons in the second wire.

2. **Given Ratio**:
- We are given that the ratio of the densities of charge carriers is:
\[ \frac{n_1}{n_2} = \frac{1}{4} \]
- This implies:
\[ n_2 = 4n_1 \]

3. **Current in Series**:
- Since the wires are connected in series, the current \( I \) flowing through both wires is the same. The current can be expressed in terms of drift velocity as:
\[ I = n_1 e A v_{d1} \quad \text{(for the first wire)} \]
\[ I = n_2 e A v_{d2} \quad \text{(for the second wire)} \]
- Here, \( e \) is the charge of an electron and \( A \) is the cross-sectional area of the wires.

4. **Equate Currents**:
- Since the currents are equal, we can set the two expressions for current equal to each other:
\[ n_1 e A v_{d1} = n_2 e A v_{d2} \]
- The area \( A \) and charge \( e \) are common and can be canceled out:
\[ n_1 v_{d1} = n_2 v_{d2} \]

5. **Express Drift Velocities**:
- Rearranging the equation gives:
\[ \frac{v_{d1}}{v_{d2}} = \frac{n_2}{n_1} \]

6. **Substitute the Density Ratio**:
- From the given ratio of densities, we have:
\[ \frac{n_2}{n_1} = \frac{4}{1} \]
- Therefore, substituting this into the equation gives:
\[ \frac{v_{d1}}{v_{d2}} = \frac{4}{1} \]

7. **Final Ratio of Drift Velocities**:
- Thus, the ratio of the drift velocities is:
\[ \frac{v_{d1}}{v_{d2}} = 4:1 \]

### Conclusion:
The drift velocities of electrons in the two wires will be in the ratio \( 4:1 \).