A : For a given conductor , electric current does not vary even if its cross sectional area varies .
R : A conductor remains unchanged when current flows through it .

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 the assertion (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that for a given conductor, the electric current does not vary even if its cross-sectional area varies.
- According to the principle of conservation of charge, the amount of charge entering a section of the conductor must equal the amount of charge leaving that section in a given time interval.

2. **Current Definition**:
- Current (I) is defined as the rate of flow of charge, mathematically represented as:
\[ I = \frac{dQ}{dT} \]
- If we assume a time interval \(dT = 1\) second, then the current can be simplified to the total charge flowing through the conductor in that time.

3. **Charge Flow in Different Sections**:
- Let’s denote the current entering through one terminal (A) as \(I\) and the current exiting through another terminal (B) as \(I'\).
- If \(Q_1\) is the charge flowing into terminal A in one second and \(Q_2\) is the charge flowing out of terminal B in one second, we have:
\[ Q_1 = I \quad \text{and} \quad Q_2 = I' \]

4. **Applying Conservation of Charge**:
- Since the conductor cannot hold charge, the charge entering must equal the charge exiting:
\[ Q_1 = Q_2 \quad \Rightarrow \quad I = I' \]
- This shows that the current remains constant regardless of the changes in the cross-sectional area of the conductor.

5. **Understanding the Reason (R)**:
- The reason states that a conductor remains unchanged when current flows through it.
- This is true because as the current flows, the entire charge entering one end of the conductor exits the other end without any accumulation of charge within the conductor itself.

6. **Conclusion**:
- Since both the assertion and the reason are true, and the reason correctly explains the assertion, we conclude that both are correct.

### Final Answer:
- Both Assertion (A) and Reason (R) are true, and R is the correct explanation for A.