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 4 A (rms) from a 240 V (rms) supply at a power factor of 0.85 lagging. Find the reactive power Q it takes.

V = 240 VI = 4 Apf = cos φ = 0.85
Q = var
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 7 A (rms) from a 230 V (rms) supply at a power factor of 0.95 lagging. Find the reactive power Q it takes.

V = 230 VI = 7 Apf = cos φ = 0.95
Q = var
3.Medium
120 VR + jXP = 2160 W20 A

An inductive load takes 20 A and 2160 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 = 20 AP = 2160 W
X = Ω
4.Medium
P = 36 kWQSφ

A single-phase motor takes 36 kW at a power factor of 0.9 lagging from a 230 V supply. Find the line current I.

P = 36 kWpf = 0.9V = 230 V
I = A
5.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.65 lagging from a 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current Inew.

P = 20 kWpf1 = 0.65pf2 = 0.92V = 230 Vf = 60 Hz
Inew = A
6.Hard
P = 45 kWQ1​S1​φ1​QC​

A single-phase load takes 45 kW at a power factor of 0.65 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the reactive power QC the capacitor must supply.

P = 45 kWpf1 = 0.65pf2 = 0.95V = 400 Vf = 60 Hz
QC = kvar

Answer key

  1. 1. Q = 505.7 var
  2. 2. Q = 502.7 var
  3. 3. X = 2.615 Ω
  4. 4. I = 173.9 A
  5. 5. Inew = 94.52 A
  6. 6. QC = 37.82 kvar

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