Lagging Power Factor
What it means
A lagging power factor happens when the current in an AC circuit lags behind the voltage. This is typical in inductive loads like motors, transformers, and fans.
- Voltage and current are sinusoidal.
- Current reaches its peak after voltage.
- This indicates the presence of inductance.
Mathematical Definition
Power Factor (PF) = cos(ฯ)
Where ฯ is the phase angle between voltage and current.
For lagging power factor: ฯ > 0 (current lags voltage)
Using Power Values
PF = Real Power (P) / Apparent Power (S)
- P = Real power (kW)
- S = Apparent power (kVA)
Using Impedance
cos(ฯ) = R / Z
- R = resistance
- Z = impedance
Example
If:
- P = 8 kW
- S = 10 kVA
PF = 8 / 10 = 0.8
If the load is inductive → 0.8 lagging power factor
Key Idea
- Lagging PF → inductive load → current lags voltage
- Leading PF → capacitive load → current leads voltage
Calculation of Resistance and Inductance
Given:
- Voltage (V) = 120 V
- Current (I) = 0.5 A
- Frequency (f) = 60 Hz
- Power Factor (cosฯ) = 0.7 (lagging)
Step 1: Calculate Impedance (Z)
Z = V / I = 120 / 0.5 = 240 ฮฉ
Step 2: Calculate Resistance (R)
R = Z × cos(ฯ) = 240 × 0.7 = 168 ฮฉ
Step 3: Calculate Inductive Reactance (XL)
XL = √(Z² − R²) = √(240² − 168²) ≈ 171.5 ฮฉ
Step 4: Calculate Inductance (L)
L = XL / (2ฯf) = 171.5 / (2 × 3.1416 × 60) ≈ 0.455 H
Final Results:
- Resistance (R) ≈ 168 ฮฉ
- Inductance (L) ≈ 0.455 H