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 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 480 V. Find the magnitude of the line current IL.

VL = 480 VZ = 4 + j3 Ω per phase
IL = A
2.Easy
ABCVL​ = 400 VIL​ = ?NZ = 6 + j8 Ωper phase

A balanced Y-connected load has an impedance of 6 + j8 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 = 6 + j8 Ω per phase
IL = A
3.Medium
ABCVL​ = 400 VIL​ = ?M55 kW, η = 95%cos φ = 0.84

A three-phase induction motor delivers 55 kW of mechanical output power at full load. At this load its efficiency is 95% and its power factor is 0.84 lagging. The supply has a line-to-line voltage of 400 V. Find the line current IL.

Pout = 55 kWη = 95%cos φ = 0.84VL = 400 V
IL = A
4.Medium
ABCVL​ = 690 VIL​ = ?M90 kW, η = 90%cos φ = 0.85

A three-phase induction motor delivers 90 kW of mechanical output power at full load. At this load its efficiency is 90% and its power factor is 0.85 lagging. The supply has a line-to-line voltage of 690 V. Find the line current IL.

Pout = 90 kWη = 90%cos φ = 0.85VL = 690 V
IL = A
5.Hard
P = 250 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 250 kW at a power factor of 0.7 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 Y. Find the capacitance Cph of each capacitor in µF.

P = 250 kWpf1 = 0.7pf2 = 0.92VL = 480 Vf = 50 Hz
Cph = µF
6.Hard
P = 50 kWφ1​S1​Q2​QC​

A balanced three-phase load takes 50 kW at a power factor of 0.75 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 = 0.75pf2 = 0.92VL = 480 Vf = 50 Hz
Cph = µF

Answer key

  1. 1. IL = 166.3 A
  2. 2. IL = 23.09 A
  3. 3. IL = 99.48 A
  4. 4. IL = 98.44 A
  5. 5. Cph = 2052 µF
  6. 6. Cph = 105 µF

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