Two electric bulbs of `40` watt each are connected in series. The power consumed by the combination will be

Options

A. 20 watt
B. 60 watt
C. 80 watt
D. 100 watt

Answer

To find the power consumed by the combination of two electric bulbs of 40 watts each connected in series, we can follow these steps:

### Step 1: Understand the Power of Each Bulb
Each bulb has a power rating of 40 watts. This means that when connected to a certain voltage (V), each bulb consumes power according to the formula:
\[ P = \frac{V^2}{R} \]
where \( P \) is the power, \( V \) is the voltage across the bulb, and \( R \) is the resistance of the bulb.

### Step 2: Calculate the Resistance of Each Bulb
From the power formula, we can rearrange it to find the resistance of each bulb:
\[ R = \frac{V^2}{P} \]
For a 40-watt bulb, if we assume it operates at a certain voltage \( V \), we can express its resistance as:
\[ R = \frac{V^2}{40} \]

### Step 3: Total Resistance in Series
When two bulbs are connected in series, the total resistance \( R_{total} \) is the sum of the individual resistances:
\[ R_{total} = R_1 + R_2 = \frac{V^2}{40} + \frac{V^2}{40} = 2 \cdot \frac{V^2}{40} = \frac{V^2}{20} \]

### Step 4: Power Consumed by the Combination
The total power consumed by the combination of the two bulbs in series can be calculated using the formula:
\[ P_{total} = \frac{V^2}{R_{total}} \]
Substituting the expression for \( R_{total} \):
\[ P_{total} = \frac{V^2}{\frac{V^2}{20}} = 20 \text{ watts} \]

### Conclusion
Thus, the power consumed by the combination of the two 40-watt bulbs connected in series is:
\[ \text{Power consumed} = 20 \text{ watts} \]

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