An electrical appliance has a rating 100 W, 120 V. The resistance of element of appliance when in use is :

Options

A. `1.2 Omega `
B. `144 Omega `
C. `120 Omega `
D. `100 Omega `

Explanation

To find the resistance of the electrical appliance, we can use the relationship between power, voltage, and resistance. Here’s the step-by-step solution:

### Step 1: Understand the given values
We are given:
- Power (P) = 100 W
- Voltage (V) = 120 V

### Step 2: Use the formula for power
The power consumed by an electrical appliance can be expressed using the formula:
\[ P = \frac{V^2}{R} \]
where:
- \( P \) is the power in watts,
- \( V \) is the voltage in volts,
- \( R \) is the resistance in ohms.

### Step 3: Rearrange the formula to solve for resistance
To find the resistance \( R \), we can rearrange the formula:
\[ R = \frac{V^2}{P} \]

### Step 4: Substitute the known values into the formula
Now, substitute the values of \( V \) and \( P \) into the equation:
\[ R = \frac{(120 \, \text{V})^2}{100 \, \text{W}} \]

### Step 5: Calculate \( V^2 \)
Calculate \( (120 \, \text{V})^2 \):
\[ (120)^2 = 14400 \, \text{V}^2 \]

### Step 6: Substitute and calculate resistance
Now substitute back into the equation:
\[ R = \frac{14400 \, \text{V}^2}{100 \, \text{W}} \]
\[ R = 144 \, \Omega \]

### Final Answer
The resistance of the element of the appliance when in use is \( 144 \, \Omega \).

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