Two bulbs `100 W, 250 V` and `200 W, 250 V` are connected in parallel across a `500 V` line. Then-

Options

A. 60 W bulb will be fused
B. 120 W bulb will be fused
C. NO bulb will be fused
D. Both bulbs will be fused

Answer

To solve the problem step by step, we need to analyze the situation of the two bulbs connected in parallel across a 500 V line.

### Step 1: Understand the given data
- Bulb A: Power (P_A) = 100 W, Voltage (V_A) = 250 V
- Bulb B: Power (P_B) = 200 W, Voltage (V_B) = 250 V
- Supply Voltage (V) = 500 V

### Step 2: Calculate the resistance of each bulb
Using the formula for power in terms of voltage and resistance, we have:
\[ P = \frac{V^2}{R} \]
From this, we can derive the resistance \( R \):
\[ R = \frac{V^2}{P} \]

#### For Bulb A:
\[ R_A = \frac{V_A^2}{P_A} = \frac{250^2}{100} = \frac{62500}{100} = 625 \, \Omega \]

#### For Bulb B:
\[ R_B = \frac{V_B^2}{P_B} = \frac{250^2}{200} = \frac{62500}{200} = 312.5 \, \Omega \]

### Step 3: Calculate the power consumed by each bulb when connected to 500 V
Using the power formula again, we can find the power consumed by each bulb when connected to the 500 V supply.

#### For Bulb A:
\[ P_A' = \frac{V^2}{R_A} = \frac{500^2}{625} = \frac{250000}{625} = 400 \, W \]

#### For Bulb B:
\[ P_B' = \frac{V^2}{R_B} = \frac{500^2}{312.5} = \frac{250000}{312.5} = 800 \, W \]

### Step 4: Determine if the bulbs will fuse
- Bulb A is rated for a maximum power of 100 W but is consuming 400 W. Therefore, Bulb A will fuse.
- Bulb B is rated for a maximum power of 200 W but is consuming 800 W. Therefore, Bulb B will also fuse.

### Conclusion
Both bulbs will fuse when connected to the 500 V supply.

### Final Answer
Both bulbs will be fused.