If the current in a heater increases by `10%` the percentage change in the power consuption

Options

A. `19%`
B. `21%`
C. `25%`
D. `17%`

Explanation

To solve the problem of finding the percentage change in power consumption when the current in a heater increases by 10%, we can follow these steps:

### Step 1: Understand the relationship between power and current
The power \( P \) consumed by a heater can be expressed using the formula:
\[ P = I^2 R \]
where \( I \) is the current and \( R \) is the resistance of the heater.

### Step 2: Determine the new current
If the current increases by 10%, the new current \( I_{\text{new}} \) can be calculated as:
\[ I_{\text{new}} = I + 0.1I = 1.1I \]

### Step 3: Calculate the new power
Using the new current, the new power \( P_{\text{new}} \) can be expressed as:
\[ P_{\text{new}} = (I_{\text{new}})^2 R = (1.1I)^2 R = 1.21 I^2 R \]

### Step 4: Calculate the old power
The old power \( P_0 \) is:
\[ P_0 = I^2 R \]

### Step 5: Find the percentage change in power
The percentage change in power is given by the formula:
\[ \text{Percentage Change} = \frac{P_{\text{new}} - P_0}{P_0} \times 100 \]
Substituting the values we have:
\[ \text{Percentage Change} = \frac{1.21 I^2 R - I^2 R}{I^2 R} \times 100 \]
This simplifies to:
\[ \text{Percentage Change} = \frac{(1.21 - 1) I^2 R}{I^2 R} \times 100 = 0.21 \times 100 = 21\% \]

### Conclusion
Thus, the percentage change in power consumption when the current increases by 10% is **21%**.

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