Power factor of an ideal choke coil (i.e. R = 0) is

Options

A. Near about zero
B. Zero
C. Near about one
D. One

Answer

To determine the power factor of an ideal choke coil, we can follow these steps:

### Step 1: Understand the Definition of Power Factor
The power factor (PF) in an AC circuit is defined as the cosine of the phase angle (φ) between the voltage and the current. It can be expressed mathematically as:
\[ \text{Power Factor} = \cos(\phi) \]

### Step 2: Identify the Components of the Choke Coil
An ideal choke coil is characterized by having zero resistance (R = 0). In an AC circuit, the total impedance (Z) is given by:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
where \( X_L \) is the inductive reactance and \( X_C \) is the capacitive reactance.

### Step 3: Substitute the Values for the Ideal Choke Coil
Since the resistance R is zero for an ideal choke coil, we can simplify the impedance equation:
\[ Z = \sqrt{0^2 + (X_L - X_C)^2} = |X_L - X_C| \]

### Step 4: Determine the Phase Angle (φ)
The phase angle φ can be determined from the relationship between resistance and reactance. Since R = 0, the angle φ becomes:
\[ \tan(\phi) = \frac{X_L - X_C}{R} \]
As R approaches zero, φ approaches 90 degrees (90°).

### Step 5: Calculate the Power Factor
Now, substituting φ into the power factor equation:
\[ \text{Power Factor} = \cos(90°) = 0 \]

### Conclusion
Thus, the power factor of an ideal choke coil (where R = 0) is:
\[ \text{Power Factor} = 0 \]