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 13 A (rms) from a 230 V (rms) supply at a power factor of 0.6 lagging. Find the real power P it takes.

V = 230 VI = 13 Apf = cos φ = 0.6
P = W
2.Easy
240 Vload28 kW, 21.5 kvarI = ?

A single-phase load connected to a 240 V supply takes 28 kW and 21.5 kvar. Find the current I drawn from the supply.

V = 240 VP = 28 kWQ = 21.5 kvar
I = A
3.Medium
P = 14 kWQSφ

A single-phase motor takes 14 kW at a power factor of 0.75 lagging from a 400 V supply. Find the line current I.

P = 14 kWpf = 0.75V = 400 V
I = A
4.Medium
230 VR + jXP = 1530 W9.5 A

An inductive load takes 9.5 A and 1530 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 = 1530 W
X = Ω
5.Hard
P1​ = 23 kWQ1​S1​φ

A 75 kVA single-phase transformer supplies a load of 23 kW at a power factor of 0.65 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 = 75 kVAP1 = 23 kWpf1 = 0.65
ΔP = kW
6.Hard
P1​ = 53 kWQ1​S1​φ

A 100 kVA single-phase transformer supplies a load of 53 kW at a power factor of 0.7 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 = 100 kVAP1 = 53 kWpf1 = 0.7
ΔP = kW

Answer key

  1. 1. P = 1794 W
  2. 2. I = 147.1 A
  3. 3. I = 46.67 A
  4. 4. X = 17.28 Ω
  5. 5. ΔP = 47.01 kW
  6. 6. ΔP = 31.12 kW

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