An electric bulb marked as 50 W-200 V is connected across a 100 V supply. The present power of the bulb is

Options

A. 37.5 W
B. 25 W
C. 12.5 W
D. 10 W

Explanation

To find the present power of the bulb when connected across a 100 V supply, we can follow these steps:

### Step 1: Understand the given values
The bulb is rated at:
- Power (P_rated) = 50 W
- Voltage (V_rated) = 220 V

The bulb is connected to a supply voltage (V_supply) of 100 V.

### Step 2: Write the formula for power consumption
The power consumed by the bulb when connected to a different voltage can be calculated using the formula:
\[ P_{actual} = \left( \frac{V_{supply}}{V_{rated}} \right)^2 \times P_{rated} \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ P_{actual} = \left( \frac{100 \, V}{220 \, V} \right)^2 \times 50 \, W \]

### Step 4: Calculate the fraction
First, calculate the fraction:
\[ \frac{100}{220} = \frac{10}{22} = \frac{5}{11} \]

### Step 5: Square the fraction
Now, square the fraction:
\[ \left( \frac{5}{11} \right)^2 = \frac{25}{121} \]

### Step 6: Multiply by the rated power
Now, multiply this result by the rated power:
\[ P_{actual} = \frac{25}{121} \times 50 \, W \]

### Step 7: Perform the multiplication
Calculating the multiplication:
\[ P_{actual} = \frac{1250}{121} \approx 10.33 \, W \]

### Step 8: Final result
Thus, the present power of the bulb when connected across a 100 V supply is approximately:
\[ P_{actual} \approx 10.33 \, W \]