Two bulbs when connected in parallel to a source take 100 W each. The total power consumed when they are connected in series with the same source is

Options

A. 25 W
B. 50 W
C. 100 W
D. 200 W

Answer

To solve the problem, we need to determine the total power consumed by two bulbs when they are connected in series after knowing their power consumption in parallel. Here’s a step-by-step solution:

### Step 1: Understand the power in parallel
When two bulbs are connected in parallel to a voltage source, each bulb consumes 100 W. This means that the voltage across each bulb is the same and equal to the source voltage \( V \).

### Step 2: Calculate the resistance of each bulb
Using the formula for power, \( P = \frac{V^2}{R} \), we can rearrange it to find the resistance:
\[ R = \frac{V^2}{P} \]
For each bulb:
\[ R_1 = \frac{V^2}{100} \quad \text{and} \quad R_2 = \frac{V^2}{100} \]

### Step 3: Calculate the equivalent resistance in series
When the bulbs are connected in series, the total resistance \( R_{eq} \) is the sum of the individual resistances:
\[ R_{eq} = R_1 + R_2 = \frac{V^2}{100} + \frac{V^2}{100} = \frac{2V^2}{100} = \frac{V^2}{50} \]

### Step 4: Calculate the total power consumed in series
The total power consumed when the bulbs are connected in series can be calculated using the formula:
\[ P = \frac{V^2}{R_{eq}} \]
Substituting \( R_{eq} \):
\[ P = \frac{V^2}{\frac{V^2}{50}} = 50 \, \text{W} \]

### Conclusion
Thus, the total power consumed when the two bulbs are connected in series is **50 W**.

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