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 7 A (rms) from a 120 V (rms) supply at a power factor of 0.95 lagging. Find the reactive power Q it takes.

V = 120 VI = 7 Apf = cos φ = 0.95
Q = var
2.Easy
P = 30.5 kWQ = 20.5 kvarS = ?φ

A load takes 30.5 kW of real power and 20.5 kvar of reactive power (lagging). Find the apparent power S.

P = 30.5 kWQ = 20.5 kvar
S = kVA
3.Medium
P = 40 kWQSφ

A single-phase motor takes 40 kW at a power factor of 0.75 lagging from a 240 V supply. Find the line current I.

P = 40 kWpf = 0.75V = 240 V
I = A
4.Medium
P = 37 kWQSφ

A single-phase motor takes 37 kW at a power factor of 0.75 lagging from a 240 V supply. Find the line current I.

P = 37 kWpf = 0.75V = 240 V
I = A
5.Hard
12 V1000 HzRs​ = 50 ΩXs​ = j5 ΩZL​ = ?

A 12 V (rms), 1000 Hz source has an internal impedance Zs = 50 + j5 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 12 V (rms)f = 1000 HzZs = 50 + j5 Ω
Pmax = W
6.Hard
12 V1000 HzRs​ = 10 ΩXs​ = j20 ΩZL​ = ?

A 12 V (rms), 1000 Hz source has an internal impedance Zs = 10 + j20 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 = 12 V (rms)f = 1000 HzZs = 10 + j20 Ω
C = µF

Answer key

  1. 1. Q = 262.3 var
  2. 2. S = 36.75 kVA
  3. 3. I = 222.2 A
  4. 4. I = 205.6 A
  5. 5. Pmax = 0.72 W
  6. 6. C = 7.958 µF

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