Assertion: The resistance of a conductor decreases with increase in cross sectional area.
Reason: On increasing the cross sectional area of a conductor, more current will flow through the conductor.

Options

A. If both assertion and reason are true and reason is the correct explantion of assertion.
B. If both assertion and reason are true and reason is not the correct explantion of assertion.
C. If assertion is false but reason is true.
D. If assertion is true but reason is false.

Explanation

To solve the assertion-reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Understand the Assertion
The assertion states that "The resistance of a conductor decreases with an increase in cross-sectional area."

- According to the formula for resistance \( R \):
\[ R = \frac{\rho L}{A} \]
where \( R \) is the resistance, \( \rho \) is the resistivity of the material, \( L \) is the length of the conductor, and \( A \) is the cross-sectional area.

- From this formula, we can see that resistance \( R \) is inversely proportional to the cross-sectional area \( A \). Therefore, if the area \( A \) increases, the resistance \( R \) decreases.

**Conclusion for Step 1**: The assertion is correct.

### Step 2: Understand the Reason
The reason states that "On increasing the cross-sectional area of a conductor, more current will flow through the conductor."

- According to Ohm's law, the current \( I \) flowing through a conductor is given by:
\[ I = \frac{V}{R} \]
where \( V \) is the voltage across the conductor.

- Since we established that increasing the cross-sectional area \( A \) decreases the resistance \( R \), it follows that if \( R \) decreases, then for a constant voltage \( V \), the current \( I \) must increase.

**Conclusion for Step 2**: The reason is also correct.

### Step 3: Determine the Relationship
Now we need to determine if the reason is the correct explanation for the assertion.

- We have established that an increase in cross-sectional area leads to a decrease in resistance. This decrease in resistance allows more current to flow through the conductor when a voltage is applied.

- Therefore, the reason directly supports the assertion by explaining how the increase in cross-sectional area affects current flow and resistance.

### Final Conclusion
Both the assertion and reason are correct, and the reason is the correct explanation for the assertion.

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