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
PQ = ?S = V·Iφ

A single-phase load draws 20 A (rms) from a 120 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 120 VI = 20 Apf = cos φ = 0.6
Q = var
2.Easy
120 Vload14.5 kW, 6 kvarI = ?

A single-phase load connected to a 120 V supply takes 14.5 kW and 6 kvar. Find the current I drawn from the supply.

V = 120 VP = 14.5 kWQ = 6 kvar
I = A
3.Medium
240 VZ16 + j12 ΩI

A load with impedance Z = 16 + j12 Ω is connected to a 240 V (rms) single-phase supply. Find the real power P it absorbs.

V = 240 VZ = 16 + j12 Ω
P = W
4.Medium
120 VR + jXP = 1674 W15.5 A

An inductive load takes 15.5 A and 1674 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 120 VI = 15.5 AP = 1674 W
R = Ω
5.Hard
P = 15 kWQ1​S1​φ1​QC​

A single-phase load takes 15 kW at a power factor of 0.65 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the reactive power QC the capacitor must supply.

P = 15 kWpf1 = 0.65pf2 = 0.9V = 400 Vf = 50 Hz
QC = kvar
6.Hard
50 V1000 HzRs​ = 50 ΩXs​ = j40 ΩZL​ = ?

A 50 V (rms), 1000 Hz source has an internal impedance Zs = 50 + j40 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 50 V (rms)f = 1000 HzZs = 50 + j40 Ω
Pmax = W

Answer key

  1. 1. Q = 1920 var
  2. 2. I = 130.8 A
  3. 3. P = 2304 W
  4. 4. R = 6.968 Ω
  5. 5. QC = 10.27 kvar
  6. 6. Pmax = 12.5 W

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