A bulb of 100W - 250V is connected to 250V mains. If another similar bulb is connected to it in series , the total power consumption is :

Options

A. 100 W
B. 200 W
C. 50 W
D. 400 W

Answer

To solve the problem of finding the total power consumption when two identical bulbs are connected in series, we can follow these steps:

### Step 1: Understand the given information
We have a bulb rated at 100W and 250V. This means that when the bulb operates at its rated voltage (250V), it consumes 100W of power.

### Step 2: Calculate the resistance of one bulb
Using the power formula, we can find the resistance of one bulb. The power (P) consumed by a bulb can be related to its voltage (V) and resistance (R) using the formula:
\[ P = \frac{V^2}{R} \]
Rearranging the formula to find R gives:
\[ R = \frac{V^2}{P} \]
Substituting the values for one bulb:
\[ R = \frac{(250)^2}{100} = \frac{62500}{100} = 625 \, \Omega \]

### Step 3: Calculate the total resistance in series
When two identical bulbs are connected in series, the total resistance (R_total) is the sum of the individual resistances:
\[ R_{total} = R_1 + R_2 = 625 \, \Omega + 625 \, \Omega = 1250 \, \Omega \]

### Step 4: Calculate the total power consumption
The total power consumed by the two bulbs in series can be calculated using the formula:
\[ P_{total} = \frac{V^2}{R_{total}} \]
Where V is the total voltage across the series connection (250V):
\[ P_{total} = \frac{(250)^2}{1250} = \frac{62500}{1250} = 50 \, W \]

### Conclusion
The total power consumption when two 100W bulbs are connected in series to a 250V mains is **50W**.

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