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 = ?QS = V·Iφ

A single-phase load draws 2 A (rms) from a 400 V (rms) supply at a power factor of 0.85 lagging. Find the real power P it takes.

V = 400 VI = 2 Apf = cos φ = 0.85
P = W
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 15 A (rms) from a 240 V (rms) supply at a power factor of 0.85 lagging. Find the real power P it takes.

V = 240 VI = 15 Apf = cos φ = 0.85
P = W
3.Medium
230 VR + jXP = 978 W5 A

An inductive load takes 5 A and 978 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 230 VI = 5 AP = 978 W
X = Ω
4.Medium
120 VZ6 + j8 ΩI

A load with impedance Z = 6 + j8 Ω is connected to a 120 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 120 VZ = 6 + j8 Ω
Q = var
5.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 kW at a power factor of 0.65 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current Inew.

P = 40 kWpf1 = 0.65pf2 = 0.9V = 400 Vf = 60 Hz
Inew = A
6.Hard
120 V60 HzRs​ = 20 ΩXs​ = j20 ΩZL​ = ?

A 120 V (rms), 60 Hz source has an internal impedance Zs = 20 + j20 Ω. The load impedance ZL can be chosen freely. The load for maximum power is built from a resistor in series with a capacitor. Find the capacitance C.

Vs = 120 V (rms)f = 60 HzZs = 20 + j20 Ω
C = µF

Answer key

  1. 1. P = 680 W
  2. 2. P = 3060 W
  3. 3. X = 24.2 Ω
  4. 4. Q = 1152 var
  5. 5. Inew = 111.1 A
  6. 6. C = 132.6 µF

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