A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

Options

A. halved
B. one - fourth
C. four times
D. doubled

Explanation

To solve the question regarding the heat generated by a heater coil that has been cut into two equal parts, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- Let the resistance of the original heater coil be \( R \).
- The heater is connected to a voltage source \( V \).

2. **Calculating Heat Generated in the Original Setup**:
- The heat generated (\( H_1 \)) in the original setup can be calculated using the formula:
\[ H_1 = \frac{V^2}{R} \times T \]
- Here, \( T \) is the time for which the heater is on.

3. **Modifying the Setup**:
- When the coil is cut into two equal parts, the resistance of each part becomes \( \frac{R}{2} \).
- We will now use only one part of the coil.

4. **Calculating Heat Generated in the Modified Setup**:
- The heat generated (\( H_2 \)) with the new resistance \( \frac{R}{2} \) can be calculated as:
\[ H_2 = \frac{V^2}{\frac{R}{2}} \times T \]
- Simplifying this gives:
\[ H_2 = \frac{2V^2}{R} \times T \]

5. **Comparing Heat Generated in Both Setups**:
- To find the relationship between \( H_2 \) and \( H_1 \), we take the ratio:
\[ \frac{H_2}{H_1} = \frac{\frac{2V^2}{R} \times T}{\frac{V^2}{R} \times T} \]
- Simplifying this ratio, we find:
\[ \frac{H_2}{H_1} = 2 \]
- This indicates that:
\[ H_2 = 2 H_1 \]

6. **Conclusion**:
- The heat generated with the cut coil (one part) is double that of the original coil. Thus, the answer to the question is that the heat generated will now be **twice the original heat generated**.

### Final Answer:
The heat generated will now be **double**.