Three identical bulbs connected in series across a source consume 20 W power. If the bulbs are connected in parallel to the same source, the power consumed is

Options

A. 20 W
B. 60 W
C. 90 W
D. 180 W

Answer

To solve the problem, we need to understand the relationship between power, resistance, and how the bulbs behave when connected in series versus parallel.

### Step-by-Step Solution:

1. **Understanding Power in Series:**
When the three identical bulbs are connected in series, the total power consumed is given as 20 W. The formula for power in terms of voltage (V) and resistance (R) is:
\[ P = \frac{V^2}{R_{\text{total}}} \]
In series, the total resistance \( R_{\text{total}} \) is the sum of the individual resistances:
\[ R_{\text{total}} = R + R + R = 3R \]
Therefore, the power consumed in series can be expressed as:
\[ P_{\text{series}} = \frac{V^2}{3R} \]
Given that \( P_{\text{series}} = 20 \, \text{W} \), we have:
\[ 20 = \frac{V^2}{3R} \quad \text{(1)} \]

2. **Understanding Power in Parallel:**
When the bulbs are connected in parallel, the total resistance \( R_{\text{parallel}} \) is given by:
\[ \frac{1}{R_{\text{parallel}}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{3}{R} \]
Therefore:
\[ R_{\text{parallel}} = \frac{R}{3} \]
The power consumed in parallel is:
\[ P_{\text{parallel}} = \frac{V^2}{R_{\text{parallel}}} = \frac{V^2}{\frac{R}{3}} = \frac{3V^2}{R} \]

3. **Relating Series and Parallel Power:**
From equation (1), we know:
\[ V^2 = 20 \times 3R = 60R \]
Now, substituting \( V^2 \) in the parallel power formula:
\[ P_{\text{parallel}} = \frac{3 \times 60R}{R} = 180 \, \text{W} \]

### Conclusion:
The power consumed when the bulbs are connected in parallel is **180 W**.