The impedance of a certain a.c. circuit is 50 ohms. If the net resistance is the circuit is 25 ohms then the power factor of the circuit will be

Options

A. Zero
B. 0.5
C. 1
D. 0.25

Explanation

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

### Step 1: Understand the given values
We are given:
- Impedance (Z) = 50 ohms
- Resistance (R) = 25 ohms

### Step 2: Recall the formula for power factor
The power factor (PF) is defined as the cosine of the phase angle (φ) between the voltage and current in an AC circuit. It can be calculated using the formula:
\[ \text{Power Factor (PF)} = \cos \phi = \frac{R}{Z} \]

### Step 3: Substitute the values into the formula
Now, we can substitute the given values of R and Z into the formula:
\[ \text{PF} = \frac{R}{Z} = \frac{25 \, \text{ohms}}{50 \, \text{ohms}} \]

### Step 4: Calculate the power factor
Now, we perform the division:
\[ \text{PF} = \frac{25}{50} = 0.5 \]

### Step 5: Final answer
The power factor of the circuit is:
\[ \text{Power Factor} = 0.5 \]