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 19 A (rms) from a 400 V (rms) supply at a power factor of 0.9 lagging. Find the real power P it takes.

V = 400 VI = 19 Apf = cos φ = 0.9
P = W
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 3 A (rms) from a 230 V (rms) supply at a power factor of 0.65 lagging. Find the real power P it takes.

V = 230 VI = 3 Apf = cos φ = 0.65
P = W
3.Medium
P = 10 kWQSφ

A single-phase motor takes 10 kW at a power factor of 0.85 lagging from a 400 V supply. Find the line current I.

P = 10 kWpf = 0.85V = 400 V
I = A
4.Medium
230 VR + jXP = 2760 W20 A

An inductive load takes 20 A and 2760 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 = 20 AP = 2760 W
X = Ω
5.Hard
100 V50 HzRs​ = 8 ΩXs​ = j20 ΩZL​ = ?

A 100 V (rms), 50 Hz source has an internal impedance Zs = 8 + 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 = 100 V (rms)f = 50 HzZs = 8 + j20 Ω
C = µF
6.Hard
240 V50 Hzload13 kW, 0.65C220 µFI

A single-phase load takes 13 kW at a power factor of 0.65 lagging from a 240 V, 50 Hz supply. A 220 µF capacitor is connected in parallel with the load. Find the new power factor cos φ seen by the supply.

P = 13 kWpf1 = 0.65V = 240 Vf = 50 HzC = 220 µF
cos φ =

Answer key

  1. 1. P = 6840 W
  2. 2. P = 448.5 W
  3. 3. I = 29.41 A
  4. 4. X = 9.2 Ω
  5. 5. C = 159.2 µF
  6. 6. cos φ = 0.7571

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