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 8 A (rms) from a 240 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 240 VI = 8 Apf = cos φ = 0.65
Q = var
2.Easy
P = 47 kWQ = 23 kvarS = ?φ

A load takes 47 kW of real power and 23 kvar of reactive power (lagging). Find the apparent power S.

P = 47 kWQ = 23 kvar
S = kVA
3.Medium
P = 16 kWQSφ

A single-phase motor takes 16 kW at a power factor of 0.6 lagging from a 230 V supply. Find the line current I.

P = 16 kWpf = 0.6V = 230 V
I = A
4.Medium
240 VR + jXP = 714 W3.5 A

An inductive load takes 3.5 A and 714 W from a 240 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 240 VI = 3.5 AP = 714 W
R = Ω
5.Hard
P = 30 kWQ1​S1​φ1​QC​

A single-phase load takes 30 kW at a power factor of 0.7 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current Inew.

P = 30 kWpf1 = 0.7pf2 = 0.92V = 230 Vf = 50 Hz
Inew = A
6.Hard
P1​ = 81 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 81 kW at a power factor of 0.75 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 = 200 kVAP1 = 81 kWpf1 = 0.75
ΔP = kW

Answer key

  1. 1. Q = 1459 var
  2. 2. S = 52.33 kVA
  3. 3. I = 115.9 A
  4. 4. R = 58.29 Ω
  5. 5. Inew = 141.8 A
  6. 6. ΔP = 105.8 kW

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