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
230 VloadP = 2691 W19.5 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 19.5 A and 2691 W. Find the power factor cos φ of the load.

V = 230 VI = 19.5 AP = 2691 W
cos φ =
2.Easy
P = ?QS = V·Iφ

A single-phase load draws 18 A (rms) from a 240 V (rms) supply at a power factor of 0.85 lagging. Find the real power P it takes.

V = 240 VI = 18 Apf = cos φ = 0.85
P = W
3.Medium
230 V12 kW, 0.85222 kW, 0.8I

Two loads are connected in parallel to a 230 V single-phase supply: a 2 kW load at a power factor of 0.85 lagging and a 22 kW load at a power factor of 0.8 lagging. Find the overall power factor cos φ seen by the supply.

V = 230 VP1 = 2 kW, pf1 = 0.85 laggingP2 = 22 kW, pf2 = 0.8 lagging
cos φ =
4.Medium
P = 8 kWQSφ

A single-phase motor takes 8 kW at a power factor of 0.8 lagging from a 230 V supply. Find the line current I.

P = 8 kWpf = 0.8V = 230 V
I = A
5.Hard
120 V50 HzRs​ = 20 ΩXs​ = j30 ΩZL​ = ?

A 120 V (rms), 50 Hz source has an internal impedance Zs = 20 + j30 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 120 V (rms)f = 50 HzZs = 20 + j30 Ω
Pmax = W
6.Hard
P = 30 kWQ1​S1​φ1​QC​

A single-phase load takes 30 kW at a power factor of 0.75 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.98. Find the capacitance C needed.

P = 30 kWpf1 = 0.75pf2 = 0.98V = 230 Vf = 50 Hz
C = µF

Answer key

  1. 1. cos φ = 0.6
  2. 2. P = 3672 W
  3. 3. cos φ = 0.8042
  4. 4. I = 43.48 A
  5. 5. Pmax = 180 W
  6. 6. C = 1225 µF

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