The element of a heater is rated (P,V). If it is connected across a source of voltage `V/2`, then the power consumed by it will be :

Options

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

Answer

To solve the problem, we need to determine the power consumed by a heater when it is connected to a voltage of \( V/2 \) instead of its rated voltage \( V \).

### Step-by-Step Solution:

1. **Understand the Rated Power and Voltage**:
The heater is rated at power \( P \) when connected to voltage \( V \). The relationship between power, voltage, and resistance is given by the formula:
\[ P = \frac{V^2}{R} \]
where \( R \) is the resistance of the heater.

2. **Calculate the Resistance**:
From the rated power equation, we can rearrange it to find the resistance \( R \):
\[ R = \frac{V^2}{P} \]

3. **Determine the New Voltage**:
The heater is now connected to a new voltage, which is \( V/2 \).

4. **Calculate the New Power**:
We need to find the new power consumed by the heater when the voltage is \( V/2 \). Using the power formula again:
\[ P' = \frac{(V/2)^2}{R} \]
Substituting \( R \) from step 2 into this equation:
\[ P' = \frac{(V/2)^2}{\frac{V^2}{P}} \]

5. **Simplify the Expression**:
Now, simplify the expression:
\[ P' = \frac{(V^2/4)}{\frac{V^2}{P}} = \frac{V^2}{4} \cdot \frac{P}{V^2} \]
This simplifies to:
\[ P' = \frac{P}{4} \]

6. **Conclusion**:
Therefore, the power consumed by the heater when connected to a voltage of \( V/2 \) is:
\[ P' = \frac{P}{4} \]

### Final Answer:
The power consumed by the heater when connected to a voltage of \( V/2 \) is \( \frac{P}{4} \).

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