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​ = 480 VIL​ = ?NZ = 5 + j12 Ωper phase

A balanced Y-connected load has an impedance of 5 + j12 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 = 5 + j12 Ω per phase
IL = A
2.Easy
ABCVL​ = 208 VIL​ = ?NZ = 9 + j12 Ωper phase

A balanced Y-connected load has an impedance of 9 + j12 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 208 V. Find the magnitude of the line current IL.

VL = 208 VZ = 9 + j12 Ω per phase
IL = A
3.Medium
ABCVL​ = 400 VZ = 18 + j24 Ωper phase

A balanced Δ-connected load with an impedance of 18 + j24 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 400 V. Find the total real power P absorbed by the load in kW.

VL = 400 VZ = 18 + j24 Ω per phase
P = kW
4.Medium
ABCVL​ = 208 VNZ = 15 + j20 Ωper phase

A balanced Y-connected load with an impedance of 15 + j20 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 208 V. Find the total real power P absorbed by the load in kW.

VL = 208 VZ = 15 + j20 Ω per phase
P = kW
5.Hard
P = 150 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 150 kW at a power factor of 0.7 lagging from a 400 V (line-to-line), 60 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.92 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 150 kWpf1 = 0.7pf2 = 0.92VL = 400 Vf = 60 Hz
Cph = µF
6.Hard
P = 50 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 50 kW at a power factor of 0.65 lagging from a 400 V (line-to-line), 60 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.92 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 50 kWpf1 = 0.65pf2 = 0.92VL = 400 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. IL = 21.32 A
  2. 2. IL = 8.006 A
  3. 3. P = 9.6 kW
  4. 4. P = 1.038 kW
  5. 5. Cph = 492.6 µF
  6. 6. Cph = 616 µF

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