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 15 A (rms) from a 400 V (rms) supply at a power factor of 0.7 lagging. Find the real power P it takes.

V = 400 VI = 15 Apf = cos φ = 0.7
P = W
2.Easy
PQ = ?S = V·Iφ

A single-phase load draws 20 A (rms) from a 240 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 240 VI = 20 Apf = cos φ = 0.6
Q = var
3.Medium
120 VZ16 + j12 ΩI

A load with impedance Z = 16 + j12 Ω is connected to a 120 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 120 VZ = 16 + j12 Ω
Q = var
4.Medium
P = 24 kWQSφ

A single-phase motor takes 24 kW at a power factor of 0.65 lagging from a 240 V supply. Find the line current I.

P = 24 kWpf = 0.65V = 240 V
I = A
5.Hard
24 V1000 HzRs​ = 25 ΩXs​ = j30 ΩZL​ = ?

A 24 V (rms), 1000 Hz source has an internal impedance Zs = 25 + j30 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 = 25 + j30 Ω
Pmax = W
6.Hard
P = 30 kWQ1​S1​φ1​QC​

A single-phase load takes 30 kW at a power factor of 0.8 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the capacitance C needed.

P = 30 kWpf1 = 0.8pf2 = 0.98V = 240 Vf = 50 Hz
C = µF

Answer key

  1. 1. P = 4200 W
  2. 2. Q = 3840 var
  3. 3. Q = 432 var
  4. 4. I = 153.8 A
  5. 5. Pmax = 5.76 W
  6. 6. C = 906.8 µF

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