Two heaters, eacch maked 1000 W, 250 V are connected in series with a 250 V supply. Assuming that their resistance remains constant, their combined rate of heating will be

Options

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

Answer

To solve the problem of finding the combined rate of heating when two heaters are connected in series, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Resistance of One Heater:**
We know the power (P) and voltage (V) for each heater. The formula relating power, voltage, and resistance is:
\[ P = \frac{V^2}{R} \]
Rearranging this gives:
\[ R = \frac{V^2}{P} \]
For each heater:
- \( V = 250 \, \text{V} \)
- \( P = 1000 \, \text{W} \)

Substituting these values:
\[ R = \frac{250^2}{1000} = \frac{62500}{1000} = 62.5 \, \Omega \]

2. **Calculate Total Resistance in Series:**
When two resistors (heaters) are connected in series, the total resistance (R_total) is the sum of their resistances:
\[ R_{\text{total}} = R_1 + R_2 = 62.5 + 62.5 = 125 \, \Omega \]

3. **Calculate the Combined Power:**
Now, we need to find the power consumed when the heaters are connected to a 250 V supply. We use the power formula again:
\[ P' = \frac{V'^2}{R_{\text{total}}} \]
Where:
- \( V' = 250 \, \text{V} \)
- \( R_{\text{total}} = 125 \, \Omega \)

Substituting these values:
\[ P' = \frac{250^2}{125} = \frac{62500}{125} = 500 \, \text{W} \]

### Final Answer:
The combined rate of heating of the two heaters connected in series with a 250 V supply is **500 W**.

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