Three electric bulbs of rating 60 W each are joined in series and then connected to electric mains. The power consumed by these three bulbs will be

Options

A. 180 W
B. 60 W
C. 20 W
D. `(20)/(3)W`

Answer

To solve the problem of finding the total power consumed by three electric bulbs of 60 W each connected in series, we can follow these steps:

### Step 1: Understand the Configuration
When electric bulbs are connected in series, the total power consumed is not simply the sum of the individual powers. Instead, we need to find the equivalent resistance of the bulbs and the current flowing through them.

**Hint:** Remember that in a series circuit, the current is the same through all components.

### Step 2: Calculate the Resistance of Each Bulb
The power rating (P) of each bulb is given as 60 W. We can use the formula for power:
\[ P = \frac{V^2}{R} \]
Where:
- \( P \) is the power (in watts),
- \( V \) is the voltage across the bulb,
- \( R \) is the resistance of the bulb.

Rearranging the formula gives us:
\[ R = \frac{V^2}{P} \]

Assuming the bulbs are rated for a standard voltage (e.g., 230 V), we can calculate the resistance of each bulb.

**Hint:** Use the standard voltage for household bulbs to find the resistance.

### Step 3: Calculate the Total Resistance in Series
Since the bulbs are in series, the total resistance \( R_{total} \) is the sum of the individual resistances:
\[ R_{total} = R_1 + R_2 + R_3 \]
Since all three bulbs have the same resistance \( R \):
\[ R_{total} = 3R \]

**Hint:** Remember that in series, resistances add up.

### Step 4: Calculate the Total Power Consumed
The total power consumed in a series circuit can be calculated using the formula:
\[ P_{total} = I^2 R_{total} \]
Where \( I \) is the current flowing through the circuit.

However, we can also express the total power in terms of the individual bulb power ratings:
\[ P_{total} = P_1 + P_2 + P_3 \]
Since each bulb is rated at 60 W:
\[ P_{total} = 60 W + 60 W + 60 W = 180 W \]

**Hint:** In series, the total power is the sum of the individual powers.

### Conclusion
The total power consumed by the three bulbs connected in series is **180 W**.

**Final Answer:** The total power consumed by the three bulbs is 180 W.