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

Options

A. `100 W` bulb with fused
B. 200 W bulb will fused
C. Both bulbs will be fused
D. No bulb will fused

Answer

To solve the problem of what happens when two bulbs (100 W, 250 V and 200 W, 250 V) are connected in parallel across a 500 V line, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Specifications of the Bulbs:**
- Bulb 1: 100 W, 250 V
- Bulb 2: 200 W, 250 V

2. **Calculate the Resistance of Each Bulb:**
- The resistance \( R \) of a bulb can be calculated using the formula:
\[ R = \frac{V^2}{P} \]
- For Bulb 1 (100 W, 250 V):
\[ R_1 = \frac{250^2}{100} = \frac{62500}{100} = 625 \, \Omega \]
- For Bulb 2 (200 W, 250 V):
\[ R_2 = \frac{250^2}{200} = \frac{62500}{200} = 312.5 \, \Omega \]

3. **Determine the Current Through Each Bulb When Connected to 500 V:**
- The current \( I \) through a bulb can be calculated using Ohm's Law:
\[ I = \frac{V}{R} \]
- For Bulb 1 (connected to 500 V):
\[ I_1 = \frac{500}{625} = 0.8 \, A \]
- For Bulb 2 (connected to 500 V):
\[ I_2 = \frac{500}{312.5} = 1.6 \, A \]

4. **Calculate the Power Dissipated by Each Bulb:**
- The power \( P \) dissipated by a bulb can be calculated using the formula:
\[ P = V \times I \]
- For Bulb 1:
\[ P_1 = 500 \times 0.8 = 400 \, W \]
- For Bulb 2:
\[ P_2 = 500 \times 1.6 = 800 \, W \]

5. **Compare the Power Dissipated with the Rated Power:**
- Bulb 1 is rated for 100 W, but it is dissipating 400 W, which exceeds its rated power.
- Bulb 2 is rated for 200 W, but it is dissipating 800 W, which also exceeds its rated power.

6. **Conclusion:**
- Both bulbs will exceed their power ratings and will fuse due to the excessive power dissipation when connected to a 500 V line.

### Final Answer:
Both bulbs will fuse.

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