If two identical heaters each rated as (1000 W, 220 V) are connected in parallel to 220 V, then the total power consumed is

Options

A. 500w
B. 2500W
C. 250W
D. 2000W

Answer

To solve the problem of finding the total power consumed by two identical heaters rated at 1000 W and 220 V connected in parallel to a 220 V supply, we can follow these steps:

### Step 1: Determine the Resistance of One Heater
The power (P) of a heater is given by the formula:
\[ P = \frac{V^2}{R} \]
Where:
- \( P \) = Power (in watts)
- \( V \) = Voltage (in volts)
- \( R \) = Resistance (in ohms)

Rearranging the formula to find the resistance \( R \):
\[ R = \frac{V^2}{P} \]

Substituting the values:
\[ R = \frac{220^2}{1000} \]

Calculating \( 220^2 \):
\[ 220^2 = 48400 \]
Thus,
\[ R = \frac{48400}{1000} = 48.4 \, \Omega \]

### Step 2: Calculate the Equivalent Resistance of Two Heaters in Parallel
For two resistors \( R_1 \) and \( R_2 \) in parallel, the equivalent resistance \( R_{eq} \) is given by:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]

Since both heaters are identical:
\[ R_1 = R_2 = R = 48.4 \, \Omega \]

Thus,
\[ \frac{1}{R_{eq}} = \frac{1}{48.4} + \frac{1}{48.4} = \frac{2}{48.4} \]
\[ R_{eq} = \frac{48.4}{2} = 24.2 \, \Omega \]

### Step 3: Calculate the Total Power Consumed
The total power consumed by the heaters can be calculated using the formula:
\[ P_{total} = \frac{V^2}{R_{eq}} \]

Substituting the values:
\[ P_{total} = \frac{220^2}{24.2} \]

Calculating \( 220^2 \) again gives us \( 48400 \):
\[ P_{total} = \frac{48400}{24.2} \]

Now, performing the division:
\[ P_{total} \approx 2000 \, W \]

### Final Answer
The total power consumed by the two heaters connected in parallel is approximately **2000 W**.

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