Two identical electric lamps marked `500 W`, `220 V` are connected in series and then joined to a `110 V` line. The power consumed by each lamp is

Options

A. `(125)/(4) W`
B. `(25)/(4) W`
C. `(225)/(4) W`
D. `125 W`

Explanation

To find the power consumed by each lamp when two identical electric lamps marked `500 W`, `220 V` are connected in series to a `110 V` line, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Connection**:
- The two lamps are connected in series, which means the total voltage of the supply (110 V) will be divided equally between the two lamps since they are identical.

2. **Calculate Voltage Across Each Lamp**:
- Since the lamps are identical, the voltage across each lamp will be:
\[ V_{lamp} = \frac{V_{total}}{2} = \frac{110 V}{2} = 55 V \]

3. **Determine the Resistance of Each Lamp**:
- The power rating and voltage rating of each lamp are given as `500 W` and `220 V`. We can use the formula for power to find the resistance:
\[ P = \frac{V^2}{R} \implies R = \frac{V^2}{P} \]
- Substituting the values:
\[ R = \frac{(220 V)^2}{500 W} = \frac{48400}{500} = 96.8 \, \Omega \]

4. **Calculate Power Consumed by Each Lamp**:
- Now that we have the resistance, we can calculate the power consumed by each lamp when 55 V is applied across it:
\[ P_{lamp} = \frac{V_{lamp}^2}{R} = \frac{(55 V)^2}{96.8 \, \Omega} \]
- Calculating this gives:
\[ P_{lamp} = \frac{3025}{96.8} \approx 31.2 \, W \]

5. **Final Result**:
- The power consumed by each lamp is approximately:
\[ P_{lamp} \approx 31.2 \, W \]

### Summary of the Solution:
- Each lamp consumes approximately **31.2 W** when connected in series to a `110 V` line.