Calculate the percentage change in power of an electric heater if the current supplied to it decreases by 2 % .

Answer

To solve the problem of calculating the percentage change in power of an electric heater when the current supplied to it decreases by 2%, we can follow these steps:

### Step 1: Understand the relationship between power and current
The power \( P \) in an electric circuit can be expressed as:
\[ P = I^2 R \]
where \( I \) is the current and \( R \) is the resistance.

### Step 2: Identify the change in current
We are given that the current decreases by 2%. This can be expressed as:
\[ \frac{\Delta I}{I} = -0.02 \]
Here, \( \Delta I \) is the change in current, and the negative sign indicates a decrease.

### Step 3: Use the formula for percentage change in power
To find the percentage change in power, we can use the relationship derived from the formula for power:
\[ \frac{\Delta P}{P} = 2 \cdot \frac{\Delta I}{I} + \frac{\Delta R}{R} \]
Since there is no change in resistance (\( \Delta R = 0 \)), the equation simplifies to:
\[ \frac{\Delta P}{P} = 2 \cdot \frac{\Delta I}{I} \]

### Step 4: Substitute the change in current into the equation
Substituting the value of \( \frac{\Delta I}{I} = -0.02 \) into the equation gives:
\[ \frac{\Delta P}{P} = 2 \cdot (-0.02) = -0.04 \]

### Step 5: Convert to percentage
To convert the change in power to a percentage, we multiply by 100:
\[ \text{Percentage change in } P = -0.04 \times 100 = -4\% \]

### Conclusion
Thus, the percentage change in power of the electric heater when the current decreases by 2% is a decrease of 4%.