The power of a heating coil is P. It is cut into two equal parts. The power of one of them across same mains is :

Options

A. P
B. 2P
C. 4P
D. `P//2`

Answer

To solve the problem, we need to determine the power of one half of a heating coil when it is connected to the same mains supply after being cut into two equal parts.

### Step-by-Step Solution:

1. **Understanding the Initial Power**:
The initial power of the heating coil is given as \( P \). The power can be expressed using the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage across the coil and \( R \) is the resistance of the coil.

2. **Resistance of the Original Coil**:
Let's denote the resistance of the original coil as \( R \). From the power formula, we can express \( R \) as:
\[ R = \frac{V^2}{P} \]

3. **Cutting the Coil**:
When the coil is cut into two equal parts, each part will have half the length of the original coil. The resistance of a wire is directly proportional to its length, so if the original length is \( L \), the length of each part will be \( \frac{L}{2} \).

4. **Calculating the Resistance of One Part**:
The resistance of one part, denoted as \( R' \), can be calculated as:
\[ R' = \frac{\rho \cdot \frac{L}{2}}{A} = \frac{R}{2} \]
where \( \rho \) is the resistivity of the material and \( A \) is the cross-sectional area of the wire. Since the cross-sectional area remains the same, the new resistance is half of the original resistance.

5. **Power of One Part**:
Now, we need to find the power of one of the cut parts when connected to the same mains. The power \( P' \) of one part can be calculated using the power formula:
\[ P' = \frac{V^2}{R'} \]
Substituting \( R' = \frac{R}{2} \) into the equation gives:
\[ P' = \frac{V^2}{\frac{R}{2}} = \frac{2V^2}{R} \]

6. **Relating New Power to Original Power**:
We know from the original power \( P = \frac{V^2}{R} \), thus:
\[ P' = 2 \cdot \frac{V^2}{R} = 2P \]

7. **Final Result**:
Therefore, the power of one of the cut parts when connected to the same mains supply is:
\[ P' = 2P \]

### Conclusion:
The power of one of the cut parts of the heating coil across the same mains is \( 2P \).

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