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
240 Vload20 kW, 6.5 kvarI = ?

A single-phase load connected to a 240 V supply takes 20 kW and 6.5 kvar. Find the current I drawn from the supply.

V = 240 VP = 20 kWQ = 6.5 kvar
I = A
2.Easy
P = 33 kWQ = 27 kvarS = ?φ

A load takes 33 kW of real power and 27 kvar of reactive power (lagging). Find the apparent power S.

P = 33 kWQ = 27 kvar
S = kVA
3.Medium
230 VZ6 + j8 ΩI

A load with impedance Z = 6 + j8 Ω is connected to a 230 V (rms) single-phase supply. Find the real power P it absorbs.

V = 230 VZ = 6 + j8 Ω
P = W
4.Medium
P = 29 kWQ = ?Sφ

A single-phase motor takes 29 kW at a power factor of 0.8 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 29 kWpf = 0.8V = 400 V
Q = kvar
5.Hard
24 V1000 HzRs​ = 2 ΩXs​ = j20 ΩZL​ = ?

A 24 V (rms), 1000 Hz source has an internal impedance Zs = 2 + j20 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 24 V (rms)f = 1000 HzZs = 2 + j20 Ω
Pmax = W
6.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 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 capacitance C needed.

P = 40 kWpf1 = 0.65pf2 = 0.92V = 230 Vf = 60 Hz
C = µF

Answer key

  1. 1. I = 87.62 A
  2. 2. S = 42.64 kVA
  3. 3. P = 3174 W
  4. 4. Q = 21.75 kvar
  5. 5. Pmax = 72 W
  6. 6. C = 1491 µF

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