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 = 31 kWQ = 10 kvarSφ

A load takes 31 kW of real power and 10 kvar of reactive power (lagging). Find the power factor cos φ.

P = 31 kWQ = 10 kvar
cos φ =
2.Easy
120 Vload14 kW, 9 kvarI = ?

A single-phase load connected to a 120 V supply takes 14 kW and 9 kvar. Find the current I drawn from the supply.

V = 120 VP = 14 kWQ = 9 kvar
I = A
3.Medium
P = 10 kWQSφ

A single-phase motor takes 10 kW at a power factor of 0.65 lagging from a 400 V supply. Find the line current I.

P = 10 kWpf = 0.65V = 400 V
I = A
4.Medium
P = 37 kWQ = ?Sφ

A single-phase motor takes 37 kW at a power factor of 0.8 lagging from a 400 V supply. Find the reactive power Q it draws.

P = 37 kWpf = 0.8V = 400 V
Q = kvar
5.Hard
10 V1000 HzRs​ = 20 ΩXs​ = j40 ΩZL​ = ?

A 10 V (rms), 1000 Hz source has an internal impedance Zs = 20 + j40 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 10 V (rms)f = 1000 HzZs = 20 + j40 Ω
Pmax = W
6.Hard
P = 50 kWQ1​S1​φ1​QC​

A single-phase load takes 50 kW at a power factor of 0.6 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the capacitance C needed.

P = 50 kWpf1 = 0.6pf2 = 0.92V = 230 Vf = 50 Hz
C = µF

Answer key

  1. 1. cos φ = 0.9517
  2. 2. I = 138.7 A
  3. 3. I = 38.46 A
  4. 4. Q = 27.75 kvar
  5. 5. Pmax = 1.25 W
  6. 6. C = 2730 µF

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