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
240 VloadP = 4212 W19.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 240 V, 19.5 A and 4212 W. Find the power factor cos φ of the load.

V = 240 VI = 19.5 AP = 4212 W
cos φ =
2.Easy
120 VloadP = 2109 W18.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 120 V, 18.5 A and 2109 W. Find the power factor cos φ of the load.

V = 120 VI = 18.5 AP = 2109 W
cos φ =
3.Medium
230 VR + jXP = 828 W6 A

An inductive load takes 6 A and 828 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 230 VI = 6 AP = 828 W
X = Ω
4.Medium
120 VR + jXP = 357 W3.5 A

An inductive load takes 3.5 A and 357 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 120 VI = 3.5 AP = 357 W
X = Ω
5.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 kW at a power factor of 0.65 lagging from a 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the capacitance C needed.

P = 5 kWpf1 = 0.65pf2 = 0.9V = 230 Vf = 60 Hz
C = µF
6.Hard
P1​ = 78 kWQ1​S1​φ

A 150 kVA single-phase transformer supplies a load of 78 kW at a power factor of 0.7 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 = 150 kVAP1 = 78 kWpf1 = 0.7
ΔP = kW

Answer key

  1. 1. cos φ = 0.9
  2. 2. cos φ = 0.95
  3. 3. X = 30.67 Ω
  4. 4. X = 18.06 Ω
  5. 5. C = 171.7 µF
  6. 6. ΔP = 49.15 kW

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