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 = 43 kWQ = 39.5 kvarS = ?φ

A load takes 43 kW of real power and 39.5 kvar of reactive power (lagging). Find the apparent power S.

P = 43 kWQ = 39.5 kvar
S = kVA
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 11 A (rms) from a 120 V (rms) supply at a power factor of 0.85 lagging. Find the real power P it takes.

V = 120 VI = 11 Apf = cos φ = 0.85
P = W
3.Medium
120 VR + jXP = 384 W4 A

An inductive load takes 4 A and 384 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 120 VI = 4 AP = 384 W
X = Ω
4.Medium
P = 6 kWQSφ

A single-phase motor takes 6 kW at a power factor of 0.8 lagging from a 240 V supply. Find the line current I.

P = 6 kWpf = 0.8V = 240 V
I = A
5.Hard
24 V60 HzRs​ = 25 ΩXs​ = j20 ΩZL​ = ?

A 24 V (rms), 60 Hz source has an internal impedance Zs = 25 + j20 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 24 V (rms)f = 60 HzZs = 25 + j20 Ω
Pmax = W
6.Hard
P1​ = 68 kWQ1​S1​φ

A 150 kVA single-phase transformer supplies a load of 68 kW at a power factor of 0.6 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

Smax = 150 kVAP1 = 68 kWpf1 = 0.6
ΔP = kW

Answer key

  1. 1. S = 58.39 kVA
  2. 2. P = 1122 W
  3. 3. X = 18 Ω
  4. 4. I = 31.25 A
  5. 5. Pmax = 5.76 W
  6. 6. ΔP = 51.5 kW

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