Assertion (A): When the radius of a copper wire is doubled, its specific resistance gets increased
Reason ( R): specific resistance is independent of cross-section of material used

Options

A. both A and R are true and R is the correct explanation of A.
B. Both A and R are true but R is not the correct explanation of A.
C. A is true but R is false
D. A is false but R is true

Answer

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

### Step 1: Understand the Assertion
The assertion states: "When the radius of a copper wire is doubled, its specific resistance gets increased."

- **Specific resistance (or resistivity)** is a property of the material itself and is defined as the resistance of a unit length of the material with a unit cross-sectional area. It is denoted by the symbol ρ (rho).
- The specific resistance is given by the formula:
\[ R = \rho \frac{L}{A} \]
where R is the resistance, L is the length, A is the cross-sectional area, and ρ is the resistivity (specific resistance).

### Step 2: Analyze the Change in Radius
When the radius of the wire is doubled:
- The area \( A \) of the wire changes as follows:
\[ A = \pi r^2 \quad \text{(original area)} \]
If the radius is doubled (new radius = 2r), the new area becomes:
\[ A' = \pi (2r)^2 = 4\pi r^2 = 4A \]
- This means the cross-sectional area increases by a factor of 4.

### Step 3: Effect on Resistance
Using the formula for resistance:
- The original resistance \( R \) is:
\[ R = \rho \frac{L}{A} \]
- The new resistance \( R' \) after doubling the radius is:
\[ R' = \rho \frac{L}{A'} = \rho \frac{L}{4A} = \frac{1}{4} \rho \frac{L}{A} = \frac{R}{4} \]
- Thus, the resistance decreases when the radius is doubled.

### Step 4: Conclusion on Assertion
Since the specific resistance (ρ) is a property of the material and does not change with the dimensions of the wire, the assertion that "specific resistance gets increased" is **incorrect**.

### Step 5: Understand the Reason
The reason states: "Specific resistance is independent of the cross-section of material used."

- This statement is **correct** because specific resistance (or resistivity) is a material property and does not depend on the dimensions or shape of the conductor.

### Final Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the correct answer is that the assertion is wrong, but the reason is correct.