Ten 60 W, 220 V bulbs are connected in series to 220 V supply . Power consumed in the circuit is

Options

A. 6W
B. 12 W
C. 180 W
D. 600 W

Answer

To solve the problem of finding the power consumed by ten 60 W, 220 V bulbs connected in series to a 220 V supply, we can follow these steps:

### Step 1: Calculate the Resistance of One Bulb
The power rating of each bulb is given as 60 W and the voltage rating 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:

\[ R = \frac{220^2}{60} \]

Calculating \( 220^2 \):

\[ 220^2 = 48400 \]

Now substituting back:

\[ R = \frac{48400}{60} \approx 806.67 \, \Omega \]

### Step 2: Calculate Total Resistance in Series
Since the bulbs are connected in series, the total resistance \( R_{total} \) is the sum of the resistances of all ten bulbs:

\[ R_{total} = 10 \times R \]

Substituting the value of \( R \):

\[ R_{total} = 10 \times 806.67 \approx 8066.67 \, \Omega \]

### Step 3: Calculate Total Power Consumed
Now we can calculate the total power consumed in the circuit using the formula:

\[ P_{total} = \frac{V_{supply}^2}{R_{total}} \]

Substituting the values:

\[ P_{total} = \frac{220^2}{8066.67} \]

Calculating:

\[ P_{total} = \frac{48400}{8066.67} \approx 6 \, W \]

### Final Answer
The power consumed in the circuit is approximately **6 W**.

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