Three-phase power worksheet with answers

Free printable Three-phase power worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
ABCVL​ = 600 VIL​ = ?NZ = 16 + j12 Ωper phase

A balanced Y-connected load has an impedance of 16 + j12 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 600 V. Find the magnitude of the line current IL.

VL = 600 VZ = 16 + j12 Ω per phase
IL = A
2.Easy
ABCVL​ = 480 VIL​ = ?NZ = 3 + j4 Ωper phase

A balanced Y-connected load has an impedance of 3 + j4 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 480 V. Find the magnitude of the line current IL.

VL = 480 VZ = 3 + j4 Ω per phase
IL = A
3.Medium
ABCVL​ = 480 VIL​ = ?M30 kW, η = 92%cos φ = 0.86

A three-phase induction motor delivers 30 kW of mechanical output power at full load. At this load its efficiency is 92% and its power factor is 0.86 lagging. The supply has a line-to-line voltage of 480 V. Find the line current IL.

Pout = 30 kWη = 92%cos φ = 0.86VL = 480 V
IL = A
4.Medium
ABCVL​ = 480 VNZ = 24 + j7 Ωper phase

A balanced Y-connected load with an impedance of 24 + j7 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 480 V. Find the total real power P absorbed by the load in kW.

VL = 480 VZ = 24 + j7 Ω per phase
P = kW
5.Hard
P = 120 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 120 kW at a power factor of 0.75 lagging from a 690 V (line-to-line), 60 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.95 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 120 kWpf1 = 0.75pf2 = 0.95VL = 690 Vf = 60 Hz
Cph = µF
6.Hard
P = 250 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 250 kW at a power factor of 0.72 lagging from a 690 V (line-to-line), 50 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.9 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 250 kWpf1 = 0.72pf2 = 0.9VL = 690 Vf = 50 Hz
Cph = µF

Answer key

  1. 1. IL = 17.32 A
  2. 2. IL = 55.43 A
  3. 3. IL = 45.61 A
  4. 4. P = 8.847 kW
  5. 5. Cph = 123.3 µF
  6. 6. Cph = 267.2 µF

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