The average power dissipated in AC circuit is 2W. If a current flowing throuh a circuit is 2A, impedance is `1Omega`, then what is the power factor of the circuit?

Options

A. `0.5`
B. 1
C. Zero
D. `1/sqrt(2)`

Explanation

To find the power factor of the AC circuit, we can follow these steps:

### Step 1: Identify the given values
- Average power (P_avg) = 2 W
- Current (I_rms) = 2 A
- Impedance (Z) = 1 Ω

### Step 2: Use the formula for average power in an AC circuit
The average power in an AC circuit is given by the formula:
\[ P_{avg} = V_{rms} \cdot I_{rms} \cdot \cos \phi \]
Where:
- \( P_{avg} \) is the average power
- \( V_{rms} \) is the root mean square voltage
- \( I_{rms} \) is the root mean square current
- \( \cos \phi \) is the power factor

### Step 3: Rearrange the formula to find \( \cos \phi \)
We can rearrange the formula to solve for the power factor \( \cos \phi \):
\[ \cos \phi = \frac{P_{avg}}{V_{rms} \cdot I_{rms}} \]

### Step 4: Calculate \( V_{rms} \)
We know that:
\[ V_{rms} = I_{rms} \cdot Z \]
Substituting the known values:
\[ V_{rms} = 2 \, \text{A} \cdot 1 \, \Omega = 2 \, \text{V} \]

### Step 5: Substitute the values into the power factor formula
Now we can substitute \( P_{avg} \), \( V_{rms} \), and \( I_{rms} \) into the rearranged formula:
\[ \cos \phi = \frac{2 \, \text{W}}{2 \, \text{V} \cdot 2 \, \text{A}} \]
\[ \cos \phi = \frac{2}{4} = 0.5 \]

### Step 6: Conclusion
The power factor of the circuit is \( 0.5 \).

### Final Answer
The power factor of the circuit is \( 0.5 \).

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