The resistance of a conductor is reduced to half its initial value. In doing so the heating effects in the conductor will become

Options

A. half
B. double
C. one-fourth
D. four times

Answer

To solve the problem, we need to analyze how the heating effect in a conductor changes when its resistance is reduced to half its initial value. The heating effect can be calculated using the formula for power and the relationship between power, resistance, and current.

### Step-by-Step Solution:

1. **Understand the Heating Effect**: The heating effect (or heat produced) in a conductor can be expressed using the formula:
\[ H = I^2 R T \]
where \( H \) is the heat produced, \( I \) is the current through the conductor, \( R \) is the resistance, and \( T \) is the time for which the current flows.

2. **Initial Resistance**: Let the initial resistance of the conductor be \( R \). Therefore, the initial heat produced can be expressed as:
\[ H_{\text{initial}} = I^2 R T \]

3. **Reduced Resistance**: When the resistance is reduced to half, the new resistance \( R' \) becomes:
\[ R' = \frac{R}{2} \]

4. **Heat with Reduced Resistance**: The heat produced with the new resistance can be calculated as:
\[ H_{\text{new}} = I^2 R' T = I^2 \left(\frac{R}{2}\right) T = \frac{I^2 R T}{2} \]

5. **Comparison of Heating Effects**: Now, we can compare the initial heat produced with the heat produced after reducing the resistance:
\[ H_{\text{new}} = \frac{H_{\text{initial}}}{2} \]
This shows that the heat produced when the resistance is halved is half of the initial heat produced.

6. **Conclusion**: Therefore, the heating effect in the conductor will become half of its initial value.

### Final Answer:
The heating effects in the conductor will become **half**.

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