If the current in an electric bulb decreases by `0.5 %`, the power in the bulb decreases by approximately

Options

A. `1 %`
B. `2 %`
C. `0.5 %`
D. `0.25 %`

Explanation

To solve the problem, we need to determine how much the power in an electric bulb decreases when the current decreases by 0.5%.

### Step-by-Step Solution:

1. **Understanding the Power Formula**:
The power (P) consumed by an electric bulb can be expressed using the formula:
\[ P = I^2 R \]
where \(I\) is the current flowing through the bulb and \(R\) is the resistance of the bulb.

2. **Identifying the Change in Current**:
We know from the problem that the current decreases by 0.5%. This can be expressed as:
\[ \Delta I = -0.005 I \]
Here, \(\Delta I\) represents the change in current.

3. **Calculating the Change in Power**:
To find the change in power (\(\Delta P\)), we can use the relationship derived from the power formula:
\[ \Delta P = P' - P \]
where \(P'\) is the new power after the decrease in current.

4. **Using the Approximation for Small Changes**:
For small changes in current, we can use the approximation:
\[ \frac{\Delta P}{P} \approx 2 \frac{\Delta I}{I} \]
This approximation is valid because the power is proportional to the square of the current.

5. **Substituting the Change in Current**:
Substituting \(\Delta I = -0.005 I\) into the equation:
\[ \frac{\Delta P}{P} \approx 2 \left(-0.005\right) = -0.01 \]

6. **Calculating the Percentage Decrease in Power**:
To express this as a percentage, we multiply by 100:
\[ \Delta P \approx -0.01 \times 100 = -1\% \]
This indicates that the power decreases by approximately 1%.

### Final Answer:
The power in the bulb decreases by approximately **1%**.

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