Power generated across a uniform wire connected across a supply is `H`. If the wire is cut into `n` equal parts and all the parts are connected in parallel across the same supply, the total power generated in the wire is

Options

A. `(H)/(n^(2))`
B. `n^(2)H`
C. `nh`
D. `(H)/(n)`

Answer

To solve the problem, we need to analyze the power generated in a uniform wire when it is cut into `n` equal parts and connected in parallel across the same supply.

### Step-by-Step Solution:

1. **Initial Power Calculation**:
- Let the original wire have a resistance \( R \) and a voltage \( V \) applied across it.
- The power generated in the wire is given by the formula:
\[ H = \frac{V^2}{R} \]

2. **Cutting the Wire**:
- When the wire is cut into `n` equal parts, the length of each part is \( \frac{L}{n} \) (where \( L \) is the original length of the wire).
- Since resistance \( R \) is directly proportional to length, the resistance of each part \( R' \) will be:
\[ R' = \frac{R}{n} \]

3. **Connecting in Parallel**:
- When these `n` parts are connected in parallel, the total resistance \( R_{total} \) of the parallel combination can be calculated using the formula for resistors in parallel:
\[ \frac{1}{R_{total}} = \frac{1}{R'} + \frac{1}{R'} + \ldots + \frac{1}{R'} \quad (n \text{ times}) \]
- This simplifies to:
\[ \frac{1}{R_{total}} = n \cdot \frac{1}{R'} = n \cdot \frac{n}{R} \implies R_{total} = \frac{R}{n^2} \]

4. **Power in the New Configuration**:
- The voltage across the parallel combination remains \( V \).
- The new power \( H' \) generated in this configuration is given by:
\[ H' = \frac{V^2}{R_{total}} = \frac{V^2}{\frac{R}{n^2}} = \frac{V^2 \cdot n^2}{R} \]
- We know from the initial case that \( H = \frac{V^2}{R} \). Therefore, we can express \( H' \) in terms of \( H \):
\[ H' = n^2 \cdot H \]

5. **Conclusion**:
- The total power generated in the wire when cut into `n` equal parts and connected in parallel is:
\[ H' = n^2 H \]

### Final Answer:
The total power generated in the wire when cut into `n` equal parts and connected in parallel is \( n^2 H \).