A heater of 1 kW and a tungsten bulb of 100 W both marked for 220 V.
The resistance of heater is:

Options

A. 50.4 `Omega`
B. 51 `Omega`
C. 48.4 `Omega`
D. 46 `Omega`

Explanation

To find the resistance of the heater, we can use the formula for electrical power, which is given by:

\[ P = \frac{V^2}{R} \]

Where:
- \( P \) is the power (in watts),
- \( V \) is the voltage (in volts),
- \( R \) is the resistance (in ohms).

### Step 1: Identify the given values
From the question, we know:
- Power of the heater, \( P = 1 \text{ kW} = 1000 \text{ W} \)
- Voltage, \( V = 220 \text{ V} \)

### Step 2: Rearrange the formula to find resistance
We need to find the resistance \( R \). Rearranging the formula gives us:

\[ R = \frac{V^2}{P} \]

### Step 3: Substitute the values into the formula
Now, we can substitute the known values into the rearranged formula:

\[ R = \frac{(220 \text{ V})^2}{1000 \text{ W}} \]

### Step 4: Calculate \( V^2 \)
Calculating \( (220)^2 \):

\[ 220^2 = 48400 \]

### Step 5: Substitute \( V^2 \) back into the equation
Now substitute \( V^2 \) back into the equation for resistance:

\[ R = \frac{48400}{1000} \]

### Step 6: Perform the division
Now, perform the division:

\[ R = 48.4 \text{ ohms} \]

### Conclusion
The resistance of the heater is \( 48.4 \text{ ohms} \).