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
PQ = ?S = V·Iφ

A single-phase load draws 5 A (rms) from a 230 V (rms) supply at a power factor of 0.7 lagging. Find the reactive power Q it takes.

V = 230 VI = 5 Apf = cos φ = 0.7
Q = var
2.Easy
P = 33 kWQ = 22 kvarS = ?φ

A load takes 33 kW of real power and 22 kvar of reactive power (lagging). Find the apparent power S.

P = 33 kWQ = 22 kvar
S = kVA
3.Medium
P = 4 kWQSφ

A single-phase motor takes 4 kW at a power factor of 0.7 lagging from a 240 V supply. Find the line current I.

P = 4 kWpf = 0.7V = 240 V
I = A
4.Medium
230 VR + jXP = 1857 W9.5 A

An inductive load takes 9.5 A and 1857 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 = 9.5 AP = 1857 W
X = Ω
5.Hard
10 V60 HzRs​ = 20 ΩXs​ = j5 ΩZL​ = ?

A 10 V (rms), 60 Hz source has an internal impedance Zs = 20 + j5 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 10 V (rms)f = 60 HzZs = 20 + j5 Ω
Pmax = W
6.Hard
P = 50 kWQ1​S1​φ1​QC​

A single-phase load takes 50 kW at a power factor of 0.8 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the new line current Inew.

P = 50 kWpf1 = 0.8pf2 = 0.95V = 240 Vf = 60 Hz
Inew = A

Answer key

  1. 1. Q = 821.3 var
  2. 2. S = 39.66 kVA
  3. 3. I = 23.81 A
  4. 4. X = 12.76 Ω
  5. 5. Pmax = 1.25 W
  6. 6. Inew = 219.3 A

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