Two heaters, each marked 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, we need to determine the combined rate of heating of two heaters connected in series with a 250 V supply. Each heater is rated at 1000 W and 250 V.

### Step-by-Step Solution:

1. **Determine the Resistance of Each Heater:**
The power (P) of each heater is given by the formula:
\[ P = \frac{V^2}{R} \]
Rearranging this formula to find resistance (R):
\[ R = \frac{V^2}{P} \]
For one heater:
\[ R = \frac{(250)^2}{1000} = \frac{62500}{1000} = 62.5 \, \Omega \]
So, the resistance of each heater is 62.5 ohms.

2. **Calculate the Total Resistance in Series:**
When resistors are connected in series, their resistances add up:
\[ R_{\text{total}} = R_1 + R_2 = 62.5 + 62.5 = 125 \, \Omega \]

3. **Calculate the Combined Rate of Heating (Power) Using the Total Resistance:**
The power consumed by the series circuit can be calculated using the formula:
\[ P = \frac{V^2}{R} \]
Here, V is the total voltage supplied (250 V) and R is the total resistance (125 Ω):
\[ P = \frac{(250)^2}{125} = \frac{62500}{125} = 500 \, W \]

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