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 8 A (rms) from a 400 V (rms) supply at a power factor of 0.65 lagging. Find the reactive power Q it takes.

V = 400 VI = 8 Apf = cos φ = 0.65
Q = var
2.Easy
120 Vload14.5 kW, 17.5 kvarI = ?

A single-phase load connected to a 120 V supply takes 14.5 kW and 17.5 kvar. Find the current I drawn from the supply.

V = 120 VP = 14.5 kWQ = 17.5 kvar
I = A
3.Medium
P = 32 kWQSφ

A single-phase motor takes 32 kW at a power factor of 0.8 lagging from a 230 V supply. Find the line current I.

P = 32 kWpf = 0.8V = 230 V
I = A
4.Medium
230 VZ16 + j12 ΩI

A load with impedance Z = 16 + j12 Ω is connected to a 230 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 230 VZ = 16 + j12 Ω
Q = var
5.Hard
120 V50 HzRs​ = 4 ΩXs​ = j30 ΩZL​ = ?

A 120 V (rms), 50 Hz source has an internal impedance Zs = 4 + j30 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 = 50 HzZs = 4 + j30 Ω
Pmax = W
6.Hard
230 V1000 HzRs​ = 5 ΩXs​ = j10 ΩZL​ = ?

A 230 V (rms), 1000 Hz source has an internal impedance Zs = 5 + j10 Ω. The load impedance ZL can be chosen freely. The load for maximum power is built from a resistor in series with a capacitor. Find the capacitance C.

Vs = 230 V (rms)f = 1000 HzZs = 5 + j10 Ω
C = µF

Answer key

  1. 1. Q = 2432 var
  2. 2. I = 189.4 A
  3. 3. I = 173.9 A
  4. 4. Q = 1587 var
  5. 5. Pmax = 900 W
  6. 6. C = 15.92 µF

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