Determine the active - reactive and apparent power:
In the given circuit, determine the active, reactive and apparent power.
Figure
Solution
The inductive reactance, X_{L} = 2π fL
= 2π × 60 × 0.2
= 75.408 Ω
Impedance, Z = 15 + j 75.408 Ω
In polar form = 76.885 ∠ 78.749^{o} Ω
Current in the Circuit
i = v/ Z = 220 ∠ 0^{o} / 76.885 ∠78.749^{o}
= 2.861 ∠ - 78.749^{o} Amp (lagging)
Power factor cos φ = cos 78.749^{o}
= 0.195 (lag)
and sin φ = sin 78.749^{o} = 0.98
Active Power
P = VI cos φ
= 220 × 2.861 × 0.195
= 122.7 Watts
or P = I^{ 2} R
Reactive Power
Q = VI sin φ
= 220 × 2.861 × 0.98
= 616.83 volt-Amp reactive or
Q = I ^{2 }X
= 617.1 VA
Apparent Power
S = VI
= 220 × 2.861
= 629.42 Volt-amp
or
= 629.2 Volt-amp.