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 11 A (rms) from a 400 V (rms) supply at a power factor of 0.9 lagging. Find the reactive power Q it takes.

V = 400 VI = 11 Apf = cos φ = 0.9
Q = var
2.Easy
230 VloadP = 1242 W9 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 9 A and 1242 W. Find the reactive power Q taken by the load.

V = 230 VI = 9 AP = 1242 W
Q = var
3.Medium
P = 39 kWQSφ

A single-phase motor takes 39 kW at a power factor of 0.75 lagging from a 400 V supply. Find the line current I.

P = 39 kWpf = 0.75V = 400 V
I = A
4.Medium
240 VZ6 + j8 ΩI

A load with impedance Z = 6 + j8 Ω is connected to a 240 V (rms) single-phase supply. Find the reactive power Q it absorbs.

V = 240 VZ = 6 + j8 Ω
Q = var
5.Hard
230 V50 Hzload5 kW, 0.6C47 µFI = ?

A single-phase load takes 5 kW at a power factor of 0.6 lagging from a 230 V, 50 Hz supply. A 47 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 5 kWpf1 = 0.6V = 230 Vf = 50 HzC = 47 µF
I = A
6.Hard
P1​ = 53 kWQ1​S1​φ

A 100 kVA single-phase transformer supplies a load of 53 kW at a power factor of 0.8 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

Smax = 100 kVAP1 = 53 kWpf1 = 0.8
ΔP = kW

Answer key

  1. 1. Q = 1918 var
  2. 2. Q = 1656 var
  3. 3. I = 130 A
  4. 4. Q = 4608 var
  5. 5. I = 33.58 A
  6. 6. ΔP = 38.76 kW

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