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​ = 208 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 208 V. Find the magnitude of the line current IL.

VL = 208 VZ = 16 + j12 Ω per phase
IL = A
2.Easy
ABCVL​ = 690 VIL​ = ?Z = 20 + j15 Ωper phase

A balanced Δ-connected load has an impedance of 20 + j15 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 690 V. Find the magnitude of the line current IL.

VL = 690 VZ = 20 + j15 Ω per phase
IL = A
3.Medium
ABCVL​ = 415 VIL​ = 40 Acos φ = 0.75lagging

A balanced three-phase load draws a line current of 40 A from a supply with a line-to-line voltage of 415 V. The power factor is 0.75 lagging. Find the total real power P drawn by the load in kW.

VL = 415 VIL = 40 Acos φ = 0.75
P = kW
4.Medium
ABCVL​ = 208 VIL​ = 20 Acos φ = 0.8lagging

A balanced three-phase load draws a line current of 20 A from a supply with a line-to-line voltage of 208 V. The power factor is 0.8 lagging. Find the total real power P drawn by the load in kW.

VL = 208 VIL = 20 Acos φ = 0.8
P = kW
5.Hard
P = 60 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 60 kW at a power factor of 0.65 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 0.92 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 60 kWpf1 = 0.65pf2 = 0.92VL = 690 Vf = 60 Hz
Cph = µF
6.Hard
P = 60 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 60 kW at a power factor of 0.8 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 0.92 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 60 kWpf1 = 0.8pf2 = 0.92VL = 690 Vf = 50 Hz
Cph = µF

Answer key

  1. 1. IL = 6.004 A
  2. 2. IL = 47.8 A
  3. 3. P = 21.56 kW
  4. 4. P = 5.764 kW
  5. 5. Cph = 248.4 µF
  6. 6. Cph = 130 µF

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