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 12 A (rms) from a 240 V (rms) supply at a power factor of 0.95 lagging. Find the reactive power Q it takes.

V = 240 VI = 12 Apf = cos φ = 0.95
Q = var
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 11 A (rms) from a 400 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 400 VI = 11 Apf = cos φ = 0.6
Q = var
3.Medium
120 VR + jXP = 384 W4 A

An inductive load takes 4 A and 384 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 120 VI = 4 AP = 384 W
R = Ω
4.Medium
P = 3 kWQ = ?Sφ

A single-phase motor takes 3 kW at a power factor of 0.65 lagging from a 230 V supply. Find the reactive power Q it draws.

P = 3 kWpf = 0.65V = 230 V
Q = kvar
5.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 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 0.98. Find the reactive power QC the capacitor must supply.

P = 40 kWpf1 = 0.7pf2 = 0.98V = 230 Vf = 50 Hz
QC = kvar
6.Hard
P = 15 kWQ1​S1​φ1​QC​

A single-phase load takes 15 kW at a power factor of 0.75 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the reactive power QC the capacitor must supply.

P = 15 kWpf1 = 0.75pf2 = 0.9V = 400 Vf = 60 Hz
QC = kvar

Answer key

  1. 1. Q = 899.3 var
  2. 2. Q = 3520 var
  3. 3. R = 24 Ω
  4. 4. Q = 3.507 kvar
  5. 5. QC = 32.69 kvar
  6. 6. QC = 5.964 kvar

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