The power of a heater is 500W at `800^(@)C`. What will be its power at `200^(@)C` it `alpha=4xx10^(-4)` per `.^(@)C`?

Explanation

To solve the problem, we need to find the power of a heater at a different temperature given its power at a specific temperature and the temperature coefficient of resistance. Here’s a step-by-step solution:

### Step 1: Understand the relationship between power and resistance
The power \( P \) of a heater can be expressed as:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage and \( R \) is the resistance. If the voltage remains constant, the power is inversely proportional to the resistance.
...