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
P = 34.5 kWQ = 14 kvarS = ?φ

A load takes 34.5 kW of real power and 14 kvar of reactive power (lagging). Find the apparent power S.

P = 34.5 kWQ = 14 kvar
S = kVA
2.Easy
400 Vload23 kW, 13 kvarI = ?

A single-phase load connected to a 400 V supply takes 23 kW and 13 kvar. Find the current I drawn from the supply.

V = 400 VP = 23 kWQ = 13 kvar
I = A
3.Medium
P = 36 kWQ = ?Sφ

A single-phase motor takes 36 kW at a power factor of 0.7 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 36 kWpf = 0.7V = 400 V
Q = kvar
4.Medium
P = 12 kWQSφ

A single-phase motor takes 12 kW at a power factor of 0.7 lagging from a 230 V supply. Find the line current I.

P = 12 kWpf = 0.7V = 230 V
I = A
5.Hard
P = 30 kWQ1​S1​φ1​QC​

A single-phase load takes 30 kW at a power factor of 0.7 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the new line current Inew.

P = 30 kWpf1 = 0.7pf2 = 0.95V = 400 Vf = 50 Hz
Inew = A
6.Hard
P1​ = 121 kWQ1​S1​φ

A 200 kVA single-phase transformer supplies a load of 121 kW at a power factor of 0.85 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 = 200 kVAP1 = 121 kWpf1 = 0.85
ΔP = kW

Answer key

  1. 1. S = 37.23 kVA
  2. 2. I = 66.05 A
  3. 3. Q = 36.73 kvar
  4. 4. I = 74.53 A
  5. 5. Inew = 78.95 A
  6. 6. ΔP = 64.41 kW

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