AC power & power factor worksheet with answers

Free printable AC power & power factor 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
P = 19.5 kWQ = 10 kvarS = ?φ

A load takes 19.5 kW of real power and 10 kvar of reactive power (lagging). Find the apparent power S.

P = 19.5 kWQ = 10 kvar
S = kVA
2.Easy
P = 47 kWQ = 12 kvarSφ

A load takes 47 kW of real power and 12 kvar of reactive power (lagging). Find the power factor cos φ.

P = 47 kWQ = 12 kvar
cos φ =
3.Medium
P = 16 kWQSφ

A single-phase motor takes 16 kW at a power factor of 0.9 lagging from a 230 V supply. Find the line current I.

P = 16 kWpf = 0.9V = 230 V
I = A
4.Medium
240 VZ5 + j12 ΩI

A load with impedance Z = 5 + j12 Ω is connected to a 240 V (rms) single-phase supply. Find the apparent power S.

V = 240 VZ = 5 + j12 Ω
S = VA
5.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.75 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the capacitance C needed.

P = 20 kWpf1 = 0.75pf2 = 0.92V = 240 Vf = 60 Hz
C = µF
6.Hard
P = 30 kWQ1​S1​φ1​QC​

A single-phase load takes 30 kW at a power factor of 0.8 lagging from a 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current Inew.

P = 30 kWpf1 = 0.8pf2 = 0.9V = 230 Vf = 60 Hz
Inew = A

Answer key

  1. 1. S = 21.91 kVA
  2. 2. cos φ = 0.9689
  3. 3. I = 77.29 A
  4. 4. S = 4431 VA
  5. 5. C = 419.9 µF
  6. 6. Inew = 144.9 A

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