An electric bulb rated 220 V, 100 W is connected in series with another bulb rated 220 V, 60 W. If the voltage across the combination is 220 V, the power consumed by the 100 W bulb will be about-

Options

A. 25 W
B. 14 W
C. 60 W
D. 100 W

Explanation

To solve the problem, we need to find the power consumed by the 100 W bulb when it is connected in series with a 60 W bulb, and the total voltage across the combination is 220 V.

### Step-by-Step Solution:

1. **Determine the Resistance of Each Bulb:**
The power (P) and voltage (V) ratings of each bulb can be used to find their resistances using the formula:
\[ R = \frac{V^2}{P} \]
For the 100 W bulb:
\[ R_1 = \frac{220^2}{100} = \frac{48400}{100} = 484 \, \Omega \]
For the 60 W bulb:
\[ R_2 = \frac{220^2}{60} = \frac{48400}{60} \approx 806.67 \, \Omega \]

2. **Calculate Total Resistance in Series:**
The total resistance (R_total) in a series circuit is the sum of the individual resistances:
\[ R_{total} = R_1 + R_2 = 484 + 806.67 \approx 1290.67 \, \Omega \]

3. **Calculate Total Current in the Circuit:**
Using Ohm's law, the total current (I) flowing through the circuit can be calculated using the total voltage (V_total = 220 V):
\[ I = \frac{V_{total}}{R_{total}} = \frac{220}{1290.67} \approx 0.170 \, A \]

4. **Calculate Power Consumed by the 100 W Bulb:**
The power consumed by the 100 W bulb can be calculated using the formula:
\[ P = I^2 R \]
Substituting the values for the 100 W bulb:
\[ P_1 = I^2 R_1 = (0.170)^2 \times 484 \approx 14.5 \, W \]

### Final Answer:
The power consumed by the 100 W bulb will be approximately **14.5 W**.