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​ = 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
2.Easy
ABCVL​ = 208 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 208 V. Find the magnitude of the line current IL.

VL = 208 VZ = 4 + j3 Ω per phase
IL = A
3.Medium
ABCVL​ = 415 VZ = 18 + j24 Ωper phase

A balanced Δ-connected load with an impedance of 18 + j24 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 415 V. Find the total real power P absorbed by the load in kW.

VL = 415 VZ = 18 + j24 Ω per phase
P = kW
4.Medium
ABCVL​ = 208 VZ = 20 + j15 Ωper phase

A balanced Δ-connected load with an impedance of 20 + j15 Ω per phase is connected to a balanced three-phase supply with a line-to-line voltage of 208 V. Find the total real power P absorbed by the load in kW.

VL = 208 VZ = 20 + j15 Ω per phase
P = kW
5.Hard
P = 120 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 120 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 0.95 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 120 kWpf1 = 0.7pf2 = 0.95VL = 415 Vf = 50 Hz
QC = kvar
6.Hard
P = 200 kWφ1​S1​Q2​QC​ = ?

A balanced three-phase load takes 200 kW at a power factor of 0.72 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 0.92 lagging. The real power stays the same. Find the total reactive power QC the capacitor bank must supply, in kvar.

P = 200 kWpf1 = 0.72pf2 = 0.92VL = 400 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. IL = 23.09 A
  2. 2. IL = 72.05 A
  3. 3. P = 10.33 kW
  4. 4. P = 4.153 kW
  5. 5. QC = 82.98 kvar
  6. 6. QC = 107.6 kvar

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