An electric bulb marked 25 W and 100 V is connected across 50 V supply . Now its power is .

Options

A. 25 W
B. 12.5 W
C. 6.25 W
D. 50 W

Answer

To find the power consumed by the electric bulb when connected to a 50 V supply, we can follow these steps:

### Step 1: Understand the given information
The electric bulb is rated at 25 W and 100 V. This means that at a voltage of 100 V, the bulb consumes 25 W of power.

### Step 2: Calculate the resistance of the bulb
Using the formula for power:
\[ P = \frac{V^2}{R} \]
We can rearrange this to find the resistance \( R \):
\[ R = \frac{V^2}{P} \]
Substituting the rated values:
\[ R = \frac{100^2}{25} = \frac{10000}{25} = 400 \, \Omega \]

### Step 3: Calculate the power when connected to a 50 V supply
Now that we have the resistance, we can find the power consumed when the bulb is connected to a 50 V supply. We use the power formula again:
\[ P = \frac{V^2}{R} \]
Substituting \( V = 50 \, V \) and \( R = 400 \, \Omega \):
\[ P = \frac{50^2}{400} = \frac{2500}{400} = 6.25 \, W \]

### Conclusion
The power consumed by the bulb when connected to a 50 V supply is **6.25 W**.

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