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
230 Vload15.5 kW, 10 kvarI = ?

A single-phase load connected to a 230 V supply takes 15.5 kW and 10 kvar. Find the current I drawn from the supply.

V = 230 VP = 15.5 kWQ = 10 kvar
I = A
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 9 A (rms) from a 120 V (rms) supply at a power factor of 0.85 lagging. Find the reactive power Q it takes.

V = 120 VI = 9 Apf = cos φ = 0.85
Q = var
3.Medium
230 VR + jXP = 1553 W9 A

An inductive load takes 9 A and 1553 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 AP = 1553 W
X = Ω
4.Medium
230 VR + jXP = 1691 W10.5 A

An inductive load takes 10.5 A and 1691 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 230 VI = 10.5 AP = 1691 W
R = Ω
5.Hard
240 V50 Hzload8 kW, 0.7C220 µFI = ?

A single-phase load takes 8 kW at a power factor of 0.7 lagging from a 240 V, 50 Hz supply. A 220 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 8 kWpf1 = 0.7V = 240 Vf = 50 HzC = 220 µF
I = A
6.Hard
P = 50 kWQ1​S1​φ1​QC​

A single-phase load takes 50 kW at a power factor of 0.65 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the capacitance C needed.

P = 50 kWpf1 = 0.65pf2 = 0.92V = 240 Vf = 60 Hz
C = µF

Answer key

  1. 1. I = 80.2 A
  2. 2. Q = 568.9 var
  3. 3. X = 16.9 Ω
  4. 4. R = 15.34 Ω
  5. 5. I = 37.61 A
  6. 6. C = 1711 µF

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