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 step by step, we will analyze how a decrease in current affects the power in an electric bulb.

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

### Step 2: Define the initial current
Let the initial current be \( I \).

### Step 3: Calculate the new current after a decrease of 0.5%
If the current decreases by 0.5%, the new current \( I' \) can be calculated as:
\[ I' = I - 0.005I = (1 - 0.005)I = 0.995I \]

### Step 4: Calculate the initial power
The initial power \( P_{initial} \) is:
\[ P_{initial} = I^2 R \]

### Step 5: Calculate the final power
The final power \( P_{final} \) with the new current \( I' \) is:
\[ P_{final} = (I')^2 R = (0.995I)^2 R = (0.995^2 I^2) R \]
Calculating \( 0.995^2 \):
\[ 0.995^2 = 0.990025 \]
Thus,
\[ P_{final} = 0.990025 I^2 R \]

### Step 6: Calculate the percentage decrease in power
The percentage decrease in power can be calculated using the formula:
\[ \text{Percentage decrease} = \frac{P_{initial} - P_{final}}{P_{initial}} \times 100 \]
Substituting the values:
\[ \text{Percentage decrease} = \frac{I^2 R - 0.990025 I^2 R}{I^2 R} \times 100 \]
This simplifies to:
\[ \text{Percentage decrease} = \frac{(1 - 0.990025) I^2 R}{I^2 R} \times 100 = (1 - 0.990025) \times 100 \]
Calculating \( 1 - 0.990025 \):
\[ 1 - 0.990025 = 0.009975 \]
Thus,
\[ \text{Percentage decrease} \approx 0.9975 \times 100 \approx 0.9975\% \]

### Conclusion
The power in the bulb decreases by approximately **1%** when the current decreases by 0.5%.