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 11 A (rms) from a 400 V (rms) supply at a power factor of 0.7 lagging. Find the reactive power Q it takes.

V = 400 VI = 11 Apf = cos φ = 0.7
Q = var
2.Easy
230 Vload19 kW, 21 kvarI = ?

A single-phase load connected to a 230 V supply takes 19 kW and 21 kvar. Find the current I drawn from the supply.

V = 230 VP = 19 kWQ = 21 kvar
I = A
3.Medium
120 VZ20 + j15 ΩI

A load with impedance Z = 20 + j15 Ω is connected to a 120 V (rms) single-phase supply. Find the real power P it absorbs.

V = 120 VZ = 20 + j15 Ω
P = W
4.Medium
120 VZ24 + j7 ΩI

A load with impedance Z = 24 + j7 Ω is connected to a 120 V (rms) single-phase supply. Find the real power P it absorbs.

V = 120 VZ = 24 + j7 Ω
P = W
5.Hard
P1​ = 59 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 59 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 = 59 kWpf1 = 0.75
ΔP = kW
6.Hard
230 V50 HzRs​ = 50 ΩXs​ = j5 ΩZL​ = ?

A 230 V (rms), 50 Hz source has an internal impedance Zs = 50 + j5 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 230 V (rms)f = 50 HzZs = 50 + j5 Ω
Pmax = W

Answer key

  1. 1. Q = 3142 var
  2. 2. I = 123.1 A
  3. 3. P = 460.8 W
  4. 4. P = 553 W
  5. 5. ΔP = 134.1 kW
  6. 6. Pmax = 264.5 W

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