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

VL = 208 VZ = 12 + j9 Ω per phase
IL = A
2.Easy
ABCVL​ = 400 VIL​ = ?NZ = 24 + j18 Ωper phase

A balanced Y-connected load has an impedance of 24 + j18 Ω per phase. It is supplied from a balanced three-phase source with a line-to-line voltage of 400 V. Find the magnitude of the line current IL.

VL = 400 VZ = 24 + j18 Ω per phase
IL = A
3.Medium
ABCVL​ = 415 VIL​ = 10 Acos φ = 0.82lagging

A balanced three-phase load draws a line current of 10 A from a supply with a line-to-line voltage of 415 V. The power factor is 0.82 lagging. Find the total real power P drawn by the load in kW.

VL = 415 VIL = 10 Acos φ = 0.82
P = kW
4.Medium
ABCVL​ = 690 VIL​ = ?M37 kW, η = 90%cos φ = 0.82

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 0.82 lagging. The supply has a line-to-line voltage of 690 V. Find the line current IL.

Pout = 37 kWη = 90%cos φ = 0.82VL = 690 V
IL = A
5.Hard
P = 80 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 80 kW at a power factor of 0.65 lagging from a 415 V (line-to-line), 60 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.98 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 = 0.65pf2 = 0.98VL = 415 Vf = 60 Hz
Cph = µF
6.Hard
P = 150 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 150 kW at a power factor of 0.78 lagging from a 415 V (line-to-line), 60 Hz supply. A three-phase capacitor bank in parallel with the load must raise the overall power factor to 0.9 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 = 0.78pf2 = 0.9VL = 415 Vf = 60 Hz
Cph = µF

Answer key

  1. 1. IL = 24.02 A
  2. 2. IL = 7.698 A
  3. 3. P = 5.894 kW
  4. 4. IL = 41.95 A
  5. 5. Cph = 1190 µF
  6. 6. Cph = 244.9 µF

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