Calculate Power Factor for Choke Coil with R and L Given

To calculate the power factor of a choke coil, you need three values:

1. The coil's resistance (R), in Ohms (Ω).
2. The coil's inductance (L), in Henrys (H).
3. The frequency (f) of the AC supply, in Hertz (Hz).

The calculation is a three-step process:

Step 1: Calculate the Inductive Reactance (X_L)
This is the opposition the coil's inductance presents to the alternating current.
X_L = 2π f L

Step 2: Calculate the Total Impedance (Z)
This is the total opposition of the coil, combining its resistance and inductive reactance.
Z = √(R² + X_L²)

Step 3: Calculate the Power Factor (cos φ)
The power factor is the ratio of the resistance to the total impedance.
cos φ = R / Z

Substituting the previous steps, the full formula is:

cos φ = R / √(R² + (2π f L)²)

Example:
A choke coil has a resistance R = 10 Ω and an inductance L = 0.1 H. It is connected to a 50 Hz supply.

1. X_L = 2π(50)(0.1) ≈ 31.42 Ω
2. Z = √(10² + 31.42²) = √(100 + 987.2) = √(1087.2) ≈ 32.97 Ω
3. cos φ = 10 / 32.97 ≈ 0.303

The power factor of this choke coil is approximately 0.303 (lagging).