Two identical heaters rated `220 V , 1000 W` are paced in series with each other across `220 V` line , then the combined power is

Options

A. 2000 W
B. 1000 W
C. 500 W
D. 250 W

Explanation

To solve the problem of finding the combined power of two identical heaters rated at 220 V and 1000 W when connected in series across a 220 V line, we can follow these steps:

### Step-by-Step Solution

1. **Determine the Resistance of Each Heater**:
- The power rating (P) of each heater is given as 1000 W, and the voltage rating (V) is 220 V.
- The resistance (R) of each heater can be calculated using the formula:
\[ P = \frac{V^2}{R} \implies R = \frac{V^2}{P} \]
- Substituting the values:
\[ R = \frac{(220)^2}{1000} = \frac{48400}{1000} = 48.4 \, \Omega \]

2. **Voltage Division in Series**:
- When two identical heaters are connected in series, the total voltage (220 V) is divided equally between them.
- Thus, the voltage across each heater (V_a) is:
\[ V_a = \frac{220 V}{2} = 110 V \]

3. **Calculate the Power Consumed by Each Heater**:
- The power consumed by each heater when the voltage across it is 110 V can be calculated using the formula:
\[ P_c = \frac{V_a^2}{R} \]
- Substituting the values:
\[ P_c = \frac{(110)^2}{48.4} = \frac{12100}{48.4} \approx 250 \, W \]

4. **Total Power Consumed by Both Heaters**:
- Since both heaters consume the same power, the total power (P_total) consumed by the two heaters is:
\[ P_{total} = P_c + P_c = 250 \, W + 250 \, W = 500 \, W \]

### Final Answer
The combined power consumed by the two heaters when placed in series across a 220 V line is **500 W**.