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

Explanation

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

### Step 1: Calculate the resistance of each bulb
The power rating (P) of each bulb is given as 100 W, and the voltage (V) is 220 V. We can use the formula for power:

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

Rearranging this formula to find the resistance (R):

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

Substituting the values:

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

### Step 2: Calculate the power drawn when the bulbs are connected in series
When two identical bulbs are connected in series, the total resistance (R_total) is:

\[ R_{\text{total}} = R + R = 2R = 2 \times 484 = 968 \, \Omega \]

The total voltage across the series combination is still 220 V. The current (I) flowing through the circuit can be calculated using Ohm's law:

\[ I = \frac{V}{R_{\text{total}}} = \frac{220}{968} \approx 0.227 \, A \]

Now, we can calculate the power (P_series) drawn by the series combination using the formula:

\[ P = I^2 R_{\text{total}} \]

Substituting the values:

\[ P_{\text{series}} = (0.227)^2 \times 968 \approx 51.5 \, W \]

### Step 3: Calculate the power drawn when the bulbs are connected in parallel
When the bulbs are connected in parallel, the voltage across each bulb remains 220 V. The power drawn by each bulb is:

\[ P_{\text{each}} = 100 \, W \]

Since there are two bulbs, the total power (P_parallel) is:

\[ P_{\text{parallel}} = 2 \times P_{\text{each}} = 2 \times 100 = 200 \, W \]

### Final Answer
The power drawn by the combination in series is approximately 51.5 W, and in parallel, it is 200 W.

### Summary of Results
- Power in series: **51.5 W**
- Power in parallel: **200 W**