Two 220 V,100 W bulbs are connected first in series and then in parallel. Each time the combination is connected to a 220 V AC supply line. The power drawn by the combination in each case respectively will be :

Options

A. 200 W, 150 W
B. 50 W , 200 W
C. 50 W , 100 W
D. 100 W , 50 W

Answer

To solve the problem of finding the power drawn by two 220 V, 100 W bulbs when connected in series and then in parallel, we can follow these steps:

### Step 1: Calculate the resistance of each bulb
The power (P) and voltage (V) of each bulb are given as 100 W and 220 V, respectively. We can use the formula for electrical power to find the resistance (R) of each bulb.

\[ R = \frac{V^2}{P} \]

Substituting the values:

\[ R = \frac{(220)^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

### Step 2: Calculate the total resistance when bulbs are connected in series
When two bulbs are connected in series, the total resistance (R_s) is the sum of the individual resistances.

\[ R_s = R + R = 2R = 2 \times 484 = 968 \, \Omega \]

### Step 3: Calculate the power drawn in series
The power drawn (P_s) when connected in series can be calculated using the formula:

\[ P_s = \frac{V^2}{R_s} \]

Substituting the values:

\[ P_s = \frac{(220)^2}{968} = \frac{48400}{968} \approx 50 \, W \]

### Step 4: Calculate the total resistance when bulbs are connected in parallel
When two bulbs are connected in parallel, the total resistance (R_p) can be calculated using the formula:

\[ \frac{1}{R_p} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \]

Thus,

\[ R_p = \frac{R}{2} = \frac{484}{2} = 242 \, \Omega \]

### Step 5: Calculate the power drawn in parallel
The power drawn (P_p) when connected in parallel can be calculated using the formula:

\[ P_p = \frac{V^2}{R_p} \]

Substituting the values:

\[ P_p = \frac{(220)^2}{242} = \frac{48400}{242} \approx 200 \, W \]

### Final Answer
The power drawn by the combination in series is approximately **50 W**, and in parallel is approximately **200 W**.

### Summary
- Power in series: **50 W**
- Power in parallel: **200 W**