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 find the total power consumed by two bulbs when they are connected in series, given that each bulb consumes 100 W when connected in parallel.

### Step-by-Step Solution:

1. **Understanding Power in Parallel:**
When the bulbs are connected in parallel, the power consumed by each bulb is given as 100 W. We can denote the power of each bulb as:
\[ P_1 = P_2 = 100 \text{ W} \]

2. **Calculating Resistance of Each Bulb:**
The power consumed by a resistive load is given by the formula:
\[ P = \frac{V^2}{R} \]
Rearranging this formula gives us the resistance:
\[ R = \frac{V^2}{P} \]
Since both bulbs consume the same power, we can denote their resistances as:
\[ R_1 = R_2 = \frac{V^2}{100} \]

3. **Total Resistance in Series:**
When the bulbs are connected in series, the total resistance \( R_{total} \) is the sum of the individual resistances:
\[ R_{total} = R_1 + R_2 = \frac{V^2}{100} + \frac{V^2}{100} = \frac{2V^2}{100} = \frac{V^2}{50} \]

4. **Calculating Total Power in Series:**
The total power consumed when the bulbs are connected in series can be calculated using the formula:
\[ P_{total} = \frac{V^2}{R_{total}} \]
Substituting \( R_{total} \):
\[ P_{total} = \frac{V^2}{\frac{V^2}{50}} = 50 \text{ W} \]

5. **Final Answer:**
Therefore, the total power consumed when the two bulbs are connected in series is:
\[ \boxed{50 \text{ W}} \]