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 solve the problem, we need to find the power consumed by a 25 W, 100 V electric bulb when it is connected to a 50 V supply. We will follow these steps:

### Step 1: Calculate the resistance of the bulb using its rated power and voltage.
The formula for power is given by:
\[ P = \frac{V_m^2}{R} \]
Where:
- \( P \) is the power (25 W)
- \( V_m \) is the marked voltage (100 V)
- \( R \) is the resistance

Rearranging the formula to find resistance \( R \):
\[ R = \frac{V_m^2}{P} \]

Substituting the values:
\[ R = \frac{100^2}{25} = \frac{10000}{25} = 400 \, \Omega \]

### Step 2: Calculate the power consumed when the bulb is connected to a 50 V supply.
Now we will use the resistance we calculated to find the power when the bulb is connected to a 50 V supply. The formula for power is:
\[ P = \frac{V_s^2}{R} \]
Where:
- \( P \) is the power
- \( V_s \) is the supply voltage (50 V)

Substituting the values:
\[ P = \frac{50^2}{400} = \frac{2500}{400} = 6.25 \, W \]

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

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