A : To a metal wire of diamete d and length L when the applied voltage is doubled, drift velocity gets doubled.
R : For a constant votage when the length is doubled, drift velocity will be halved but drift velocity is independent of diameter .

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion then mark.
C. If Assertion is ture statement but Reason is false , then mark
D. If both Assertion and Reason are false statements then mark.

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding Assertion (A)**:
- The assertion states that when the applied voltage (V) across a metal wire of diameter (d) and length (L) is doubled, the drift velocity (Vd) also gets doubled.
- We know that the relationship between current (I), drift velocity (Vd), and other parameters is given by the equation:
\[ I = N \cdot E \cdot A \cdot Vd \]
where:
- \(N\) = number density of charge carriers
- \(E\) = charge of the electron
- \(A\) = cross-sectional area of the wire
- \(Vd\) = drift velocity

2. **Using Ohm's Law**:
- According to Ohm's Law, we have:
\[ I = \frac{V}{R} \]
- The resistance \(R\) can be expressed as:
\[ R = \rho \cdot \frac{L}{A} \]
where \(\rho\) is the resistivity of the material.

3. **Relating Voltage, Length, and Drift Velocity**:
- Substituting \(R\) into the equation for current gives:
\[ I = \frac{V \cdot A}{\rho \cdot L} \]
- Setting the two expressions for current equal gives:
\[ \frac{V \cdot A}{\rho \cdot L} = N \cdot E \cdot A \cdot Vd \]
- Canceling \(A\) from both sides leads to:
\[ \frac{V}{\rho \cdot L} = N \cdot E \cdot Vd \]
- Rearranging this gives us:
\[ Vd = \frac{V}{\rho \cdot N \cdot E \cdot L} \]

4. **Analyzing the Effect of Doubling Voltage**:
- If the voltage is doubled (let's denote the new voltage as \(V' = 2V\)), while keeping \(L\) constant:
\[ Vd' = \frac{2V}{\rho \cdot N \cdot E \cdot L} \]
- This shows that \(Vd' = 2Vd\), confirming that the drift velocity indeed doubles when the voltage is doubled.

5. **Understanding Reason (R)**:
- The reason states that for a constant voltage, if the length is doubled, the drift velocity will be halved, and that drift velocity is independent of diameter.
- If we set \(V' = V\) and \(L' = 2L\):
\[ Vd' = \frac{V}{\rho \cdot N \cdot E \cdot 2L} = \frac{Vd}{2} \]
- This confirms that the drift velocity is halved when the length is doubled while keeping voltage constant.

6. **Independence from Diameter**:
- The drift velocity does not depend on the diameter of the wire, as seen from the equations derived. It only depends on the voltage and the length of the wire.

### Conclusion:
- Both the assertion (A) and the reason (R) are true.
- However, the reason does not correctly explain the assertion, as the assertion deals with the effect of voltage change while the reason deals with the effect of length change.

### Final Answer:
- The correct option is that both assertion and reason are true, but the reason is not the correct explanation for the assertion.