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 = 16.5 kWQ = 17.5 kvarSφ

A load takes 16.5 kW of real power and 17.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 16.5 kWQ = 17.5 kvar
cos φ =
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 17 A (rms) from a 230 V (rms) supply at a power factor of 0.75 lagging. Find the reactive power Q it takes.

V = 230 VI = 17 Apf = cos φ = 0.75
Q = var
3.Medium
P = 25 kWQ = ?Sφ

A single-phase motor takes 25 kW at a power factor of 0.75 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 25 kWpf = 0.75V = 400 V
Q = kvar
4.Medium
230 VR + jXP = 1104 W8 A

An inductive load takes 8 A and 1104 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 = 8 AP = 1104 W
X = Ω
5.Hard
100 V1000 HzRs​ = 5 ΩXs​ = j20 ΩZL​ = ?

A 100 V (rms), 1000 Hz source has an internal impedance Zs = 5 + j20 Ω. The load impedance ZL can be chosen freely. The load for maximum power is built from a resistor in series with a capacitor. Find the capacitance C.

Vs = 100 V (rms)f = 1000 HzZs = 5 + j20 Ω
C = µF
6.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 kW at a power factor of 0.6 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the new line current Inew.

P = 5 kWpf1 = 0.6pf2 = 0.9V = 400 Vf = 50 Hz
Inew = A

Answer key

  1. 1. cos φ = 0.686
  2. 2. Q = 2586 var
  3. 3. Q = 22.05 kvar
  4. 4. X = 23 Ω
  5. 5. C = 7.958 µF
  6. 6. Inew = 13.89 A

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