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​ = 690 VZ = 12 + j9 Ωper phase

A balanced Δ-connected load has an impedance of 12 + j9 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 phase current Iph flowing through each impedance.

VL = 690 VZ = 12 + j9 Ω per phase
Iph = A
2.Easy
ABCVL​ = 208 VIL​ = ?NZ = 12 + j16 Ωper phase

A balanced Y-connected load has an impedance of 12 + j16 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 = 12 + j16 Ω per phase
IL = A
3.Medium
ABCVL​ = 415 VIL​ = ?M37 kW, η = 90%cos φ = 0.88

A three-phase induction motor delivers 37 kW of mechanical output power at full load. At this load its efficiency is 90% and its power factor is 0.88 lagging. The supply has a line-to-line voltage of 415 V. Find the line current IL.

Pout = 37 kWη = 90%cos φ = 0.88VL = 415 V
IL = A
4.Medium
ABCVL​ = 415 VIL​ = ?M75 kW, η = 90%cos φ = 0.86

A three-phase induction motor delivers 75 kW of mechanical output power at full load. At this load its efficiency is 90% and its power factor is 0.86 lagging. The supply has a line-to-line voltage of 415 V. Find the line current IL.

Pout = 75 kWη = 90%cos φ = 0.86VL = 415 V
IL = A
5.Hard
P = 80 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 80 kW at a power factor of 0.8 lagging from a 400 V (line-to-line), 50 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.95 lagging. The real power stays the same. The capacitors are connected in Y. Find the capacitance Cph of each capacitor in µF.

P = 80 kWpf1 = 0.8pf2 = 0.95VL = 400 Vf = 50 Hz
Cph = µF
6.Hard
P = 80 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 80 kW at a power factor of 0.78 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 = 80 kWpf1 = 0.78pf2 = 0.92VL = 400 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. Iph = 46 A
  2. 2. IL = 6.004 A
  3. 3. IL = 64.99 A
  4. 4. IL = 134.8 A
  5. 5. Cph = 670.5 µF
  6. 6. Cph = 499.1 µF

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