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 = ?QS = V·Iφ

A single-phase load draws 2 A (rms) from a 400 V (rms) supply at a power factor of 0.65 lagging. Find the real power P it takes.

V = 400 VI = 2 Apf = cos φ = 0.65
P = W
2.Easy
230 VloadP = 1121 W6.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 6.5 A and 1121 W. Find the power factor cos φ of the load.

V = 230 VI = 6.5 AP = 1121 W
cos φ =
3.Medium
230 VZ12 + j9 ΩI

A load with impedance Z = 12 + j9 Ω is connected to a 230 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 230 VZ = 12 + j9 Ω
Q = var
4.Medium
P = 20 kWQSφ

A single-phase motor takes 20 kW at a power factor of 0.6 lagging from a 230 V supply. Find the line current I.

P = 20 kWpf = 0.6V = 230 V
I = A
5.Hard
100 V1000 HzRs​ = 4 ΩXs​ = j10 ΩZL​ = ?

A 100 V (rms), 1000 Hz source has an internal impedance Zs = 4 + j10 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 100 V (rms)f = 1000 HzZs = 4 + j10 Ω
Pmax = W
6.Hard
P = 35 kWQ1​S1​φ1​QC​

A single-phase load takes 35 kW at a power factor of 0.8 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the capacitance C needed.

P = 35 kWpf1 = 0.8pf2 = 0.95V = 400 Vf = 60 Hz
C = µF

Answer key

  1. 1. P = 520 W
  2. 2. cos φ = 0.7498
  3. 3. Q = 2116 var
  4. 4. I = 144.9 A
  5. 5. Pmax = 625 W
  6. 6. C = 244.5 µF

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