Step-by-step explanation:
KVA power input = 20.
Power kW input = 11.
power factor = Cos φ = 11/20 = 0.55, Φ = 56.63°.
Line current = I = 25A = phase current.
Real power = 11 kW = 3 I² R = 3 Iph × Vph × Cos φ
=> R = 11000/(3×25² ) = 5.87 Ohm.
Phase voltage RMS = Vph = kW /(3 I Cosφ)
= 11000/ (3 × 25 × 0.55) = 266.67 V.
Line voltage Vʟ= √3 × Vph = 461.87 V.
(ii) KVAR input = √(20² - 11²) = 3 √31 = reactive power.
f = 60Hz. ω = 2π f = 120π rad/s.
3 I² Zi = 3√31 × 1000
Zi = √31 ×1000 ÷ 25² = 8.91 Ohm.
Zi = ω L
=> L = 23.64 μH.
(iii) Resistance = R = 5.87 Ohm.
Reactance = √(R²+ ω² L²) = 10.67 Ohm.