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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
ABCVL​ = 480 VZ = 16 + j12 Ωper phase

A balanced Δ-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 480 V. Find the magnitude of the phase current Iph flowing through each impedance.

VL = 480 VZ = 16 + j12 Ω per phase
Iph = A
2.Easy
ABCVL​ = 208 VZ = 7 + j24 Ωper phase

A balanced Δ-connected load has an impedance of 7 + j24 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 phase current Iph flowing through each impedance.

VL = 208 VZ = 7 + j24 Ω per phase
Iph = A
3.Medium
ABCVL​ = 415 VIL​ = ?M30 kW, η = 91%cos φ = 0.84

A three-phase induction motor delivers 30 kW of mechanical output power at full load. At this load its efficiency is 91% and its power factor is 0.84 lagging. The supply has a line-to-line voltage of 415 V. Find the line current IL.

Pout = 30 kWη = 91%cos φ = 0.84VL = 415 V
IL = A
4.Medium
ABCVL​ = 415 VIL​ = ?M15 kW, η = 95%cos φ = 0.85

A three-phase induction motor delivers 15 kW of mechanical output power at full load. At this load its efficiency is 95% and its power factor is 0.85 lagging. The supply has a line-to-line voltage of 415 V. Find the line current IL.

Pout = 15 kWη = 95%cos φ = 0.85VL = 415 V
IL = A
5.Hard
P = 60 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 60 kW at a power factor of 0.72 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 0.95 lagging. The real power stays the same. The capacitors are connected in Δ. Find the capacitance Cph of each capacitor in µF.

P = 60 kWpf1 = 0.72pf2 = 0.95VL = 400 Vf = 60 Hz
Cph = µF
6.Hard
P = 300 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 300 kW at a power factor of 0.78 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 0.98 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 300 kWpf1 = 0.78pf2 = 0.98VL = 400 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. Iph = 24 A
  2. 2. Iph = 8.32 A
  3. 3. IL = 54.6 A
  4. 4. IL = 25.84 A
  5. 5. Cph = 210.6 µF
  6. 6. QC = 179.8 kvar

Full step-by-step solutions: practise this topic on examproblems.com.