Assertion : A resistance wire is broken into four pices and all are connected in parallel. Then, net resistance becomes 1/16 times.
Reason : In parallel net resistance is less than the smallest value of individual resistance.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true and Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the problem, we need to analyze the assertion and the reason provided regarding the resistance of a wire that is broken into four pieces and connected in parallel.

### Step-by-Step Solution:

1. **Understanding the Resistance of the Wire**:
- Let the original resistance of the wire be \( R \).
- The resistance of a wire is given by the formula:
\[ R = \frac{\rho L}{A} \]
- Here, \( \rho \) is the resistivity, \( L \) is the length, and \( A \) is the cross-sectional area.

2. **Breaking the Wire into Four Pieces**:
- When the wire is broken into four equal pieces, the length of each piece becomes \( \frac{L}{4} \).
- The resistance of each piece can be calculated as:
\[ R_{individual} = \frac{\rho \left(\frac{L}{4}\right)}{A} = \frac{R}{4} \]
- Therefore, each of the four pieces has a resistance of \( \frac{R}{4} \).

3. **Connecting the Pieces in Parallel**:
- When resistors are connected in parallel, the equivalent resistance \( R_{eq} \) can be calculated using the formula:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} \]
- Since all four pieces have the same resistance \( \frac{R}{4} \):
\[ \frac{1}{R_{eq}} = \frac{1}{\frac{R}{4}} + \frac{1}{\frac{R}{4}} + \frac{1}{\frac{R}{4}} + \frac{1}{\frac{R}{4}} = 4 \cdot \frac{4}{R} = \frac{16}{R} \]
- Therefore, the equivalent resistance is:
\[ R_{eq} = \frac{R}{16} \]

4. **Conclusion on Assertion**:
- The assertion states that the net resistance becomes \( \frac{1}{16} \) times the original resistance, which we have confirmed is true since \( R_{eq} = \frac{R}{16} \).

5. **Analyzing the Reason**:
- The reason states that in parallel, the net resistance is less than the smallest value of individual resistance.
- This is also true because the equivalent resistance \( R_{eq} \) is indeed less than \( \frac{R}{4} \) (the smallest individual resistance).

6. **Final Evaluation**:
- The assertion is correct, and the reason is also correct. However, the reason does not directly explain why the assertion is true in this specific case (the factor of \( \frac{1}{16} \)).
- Therefore, while both statements are true, the reason does not serve as a correct explanation for the assertion.

### Final Answer:
- Assertion: True
- Reason: True, but not a correct explanation of the assertion.