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 = 22 kWQ = 24.5 kvarSφ

A load takes 22 kW of real power and 24.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 22 kWQ = 24.5 kvar
cos φ =
2.Easy
400 Vload16 kW, 6 kvarI = ?

A single-phase load connected to a 400 V supply takes 16 kW and 6 kvar. Find the current I drawn from the supply.

V = 400 VP = 16 kWQ = 6 kvar
I = A
3.Medium
230 VR + jXP = 2737 W14 A

An inductive load takes 14 A and 2737 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 = 14 AP = 2737 W
X = Ω
4.Medium
P = 21 kWQSφ

A single-phase motor takes 21 kW at a power factor of 0.6 lagging from a 240 V supply. Find the line current I.

P = 21 kWpf = 0.6V = 240 V
I = A
5.Hard
P = 30 kWQ1​S1​φ1​QC​

A single-phase load takes 30 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 0.92. Find the new line current Inew.

P = 30 kWpf1 = 0.65pf2 = 0.92V = 230 Vf = 60 Hz
Inew = A
6.Hard
P = 30 kWQ1​S1​φ1​QC​

A single-phase load takes 30 kW at a power factor of 0.8 lagging from a 230 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the capacitance C needed.

P = 30 kWpf1 = 0.8pf2 = 0.92V = 230 Vf = 60 Hz
C = µF

Answer key

  1. 1. cos φ = 0.6681
  2. 2. I = 42.72 A
  3. 3. X = 8.654 Ω
  4. 4. I = 145.8 A
  5. 5. Inew = 141.8 A
  6. 6. C = 487.4 µF

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