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 = 24 + j7 Ωper phase

A balanced Y-connected load has an impedance of 24 + j7 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 = 24 + j7 Ω per phase
IL = A
2.Easy
ABCVL​ = 600 VIL​ = ?Z = 4 + j3 Ωper phase

A balanced Δ-connected load has an impedance of 4 + j3 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 = 4 + j3 Ω per phase
IL = A
3.Medium
ABCVL​ = 480 VIL​ = ?M110 kW, η = 94%cos φ = 0.86

A three-phase induction motor delivers 110 kW of mechanical output power at full load. At this load its efficiency is 94% 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 = 110 kWη = 94%cos φ = 0.86VL = 480 V
IL = A
4.Medium
ABCVL​ = 480 VIL​ = ?M75 kW, η = 93%cos φ = 0.85

A three-phase induction motor delivers 75 kW of mechanical output power at full load. At this load its efficiency is 93% and its power factor is 0.85 lagging. The supply has a line-to-line voltage of 480 V. Find the line current IL.

Pout = 75 kWη = 93%cos φ = 0.85VL = 480 V
IL = A
5.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 480 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 Δ. Find the capacitance Cph of each capacitor in µF.

P = 50 kWpf1 = 0.65pf2 = 0.92VL = 480 Vf = 50 Hz
Cph = µF
6.Hard
P = 75 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 75 kW at a power factor of 0.7 lagging from a 415 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. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 75 kWpf1 = 0.7pf2 = 0.92VL = 415 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. IL = 11.09 A
  2. 2. IL = 207.8 A
  3. 3. IL = 163.7 A
  4. 4. IL = 114.1 A
  5. 5. Cph = 171.1 µF
  6. 6. QC = 44.57 kvar

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