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 3 A (rms) from a 240 V (rms) supply at a power factor of 0.65 lagging. Find the real power P it takes.

V = 240 VI = 3 Apf = cos φ = 0.65
P = W
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 18 A (rms) from a 400 V (rms) supply at a power factor of 0.9 lagging. Find the real power P it takes.

V = 400 VI = 18 Apf = cos φ = 0.9
P = W
3.Medium
P = 36 kWQSφ

A single-phase motor takes 36 kW at a power factor of 0.7 lagging from a 230 V supply. Find the line current I.

P = 36 kWpf = 0.7V = 230 V
I = A
4.Medium
P = 29 kWQ = ?Sφ

A single-phase motor takes 29 kW at a power factor of 0.7 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 29 kWpf = 0.7V = 400 V
Q = kvar
5.Hard
120 V1000 HzRs​ = 20 ΩXs​ = j3 ΩZL​ = ?

A 120 V (rms), 1000 Hz source has an internal impedance Zs = 20 + j3 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 120 V (rms)f = 1000 HzZs = 20 + j3 Ω
Pmax = W
6.Hard
P = 50 kWQ1​S1​φ1​QC​

A single-phase load takes 50 kW at a power factor of 0.75 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the reactive power QC the capacitor must supply.

P = 50 kWpf1 = 0.75pf2 = 0.92V = 400 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. P = 468 W
  2. 2. P = 6480 W
  3. 3. I = 223.6 A
  4. 4. Q = 29.59 kvar
  5. 5. Pmax = 180 W
  6. 6. QC = 22.8 kvar

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