Some electric bulbs are connected in series across a 220 V supply in a room. If one bulb is fused then remaining bulbs are connected again in series across the same supply. The illumination in the room will

Options

A. increase
B. decrease
C. remain the same
D. not continuous

Answer

To solve the problem step by step, we will analyze the situation of electric bulbs connected in series and how the illumination changes when one bulb is fused.

### Step 1: Understand the Initial Setup
Initially, we have three bulbs connected in series across a 220 V supply. Let's denote the resistance of each bulb as \( R \). Therefore, the total resistance \( R_{total} \) of the circuit with three bulbs is:
\[ R_{total} = R + R + R = 3R \]

### Step 2: Calculate the Initial Current
Using Ohm's law, the current \( I \) flowing through the circuit can be calculated as:
\[ I = \frac{V}{R_{total}} = \frac{220 \, V}{3R} \]

### Step 3: Calculate the Initial Power
The power \( P \) consumed by the circuit can be calculated using the formula:
\[ P = I^2 R_{total} \]
Substituting the expression for current:
\[ P = \left(\frac{220}{3R}\right)^2 \times 3R = \frac{220^2}{3R} \times 3 = \frac{220^2}{R} \]

### Step 4: Analyze the Situation When One Bulb Fuses
When one bulb fuses, only two bulbs remain in the circuit. The new total resistance \( R'_{total} \) is:
\[ R'_{total} = R + R = 2R \]

### Step 5: Calculate the New Current
The new current \( I' \) flowing through the circuit with two bulbs is:
\[ I' = \frac{V}{R'_{total}} = \frac{220 \, V}{2R} \]

### Step 6: Calculate the New Power
The new power \( P' \) consumed by the circuit with two bulbs can be calculated as:
\[ P' = I'^2 R'_{total} \]
Substituting the expression for the new current:
\[ P' = \left(\frac{220}{2R}\right)^2 \times 2R = \frac{220^2}{4R} \times 2 = \frac{220^2}{2R} \]

### Step 7: Compare the Powers
Now, we can compare the initial power \( P \) and the new power \( P' \):
- Initial power: \( P = \frac{220^2}{R} \)
- New power: \( P' = \frac{220^2}{2R} \)

Since \( P' = \frac{1}{2} P \), the power consumed when one bulb is fused is half of the initial power.

### Conclusion
When one bulb is fused, the remaining bulbs connected in series will result in decreased illumination because the power consumed is reduced.

### Final Answer
The illumination in the room will decrease.

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