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 0.7 lagging. Find the reactive power Q it takes.

V = 120 VI = 7 Apf = cos φ = 0.7
Q = var
2.Easy
400 Vload8.5 kW, 7.5 kvarI = ?

A single-phase load connected to a 400 V supply takes 8.5 kW and 7.5 kvar. Find the current I drawn from the supply.

V = 400 VP = 8.5 kWQ = 7.5 kvar
I = A
3.Medium
240 VR + jXP = 720 W5 A

An inductive load takes 5 A and 720 W from a 240 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 240 VI = 5 AP = 720 W
R = Ω
4.Medium
P = 23 kWQSφ

A single-phase motor takes 23 kW at a power factor of 0.6 lagging from a 240 V supply. Find the line current I.

P = 23 kWpf = 0.6V = 240 V
I = A
5.Hard
P = 5 kWQ1​S1​φ1​QC​

A single-phase load takes 5 kW at a power factor of 0.75 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current Inew.

P = 5 kWpf1 = 0.75pf2 = 0.92V = 240 Vf = 50 Hz
Inew = A
6.Hard
P = 20 kWQ1​S1​φ1​QC​

A single-phase load takes 20 kW at a power factor of 0.7 lagging from a 240 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the capacitance C needed.

P = 20 kWpf1 = 0.7pf2 = 0.95V = 240 Vf = 50 Hz
C = µF

Answer key

  1. 1. Q = 599.9 var
  2. 2. I = 28.34 A
  3. 3. R = 28.8 Ω
  4. 4. I = 159.7 A
  5. 5. Inew = 22.64 A
  6. 6. C = 764.3 µF

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