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 = ?QS = V·Iφ

A single-phase load draws 20 A (rms) from a 230 V (rms) supply at a power factor of 0.8 lagging. Find the real power P it takes.

V = 230 VI = 20 Apf = cos φ = 0.8
P = W
2.Easy
230 VloadP = 518 W3 A

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 3 A and 518 W. Find the power factor cos φ of the load.

V = 230 VI = 3 AP = 518 W
cos φ =
3.Medium
400 V14 kW, 0.85210 kW, 0.9I = ?

Two loads are connected in parallel to a 400 V single-phase supply: a 4 kW load at a power factor of 0.85 lagging and a 10 kW load at a power factor of 0.9 lagging. Find the total current I drawn from the supply.

V = 400 VP1 = 4 kW, pf1 = 0.85 laggingP2 = 10 kW, pf2 = 0.9 lagging
I = A
4.Medium
P = 16 kWQ = ?Sφ

A single-phase motor takes 16 kW at a power factor of 0.75 lagging from a 240 V supply. Find the reactive power Q it draws.

P = 16 kWpf = 0.75V = 240 V
Q = kvar
5.Hard
50 V60 HzRs​ = 10 ΩXs​ = j20 ΩZL​ = ?

A 50 V (rms), 60 Hz source has an internal impedance Zs = 10 + j20 Ω. The load impedance ZL can be chosen freely. The load for maximum power is built from a resistor in series with a capacitor. Find the capacitance C.

Vs = 50 V (rms)f = 60 HzZs = 10 + j20 Ω
C = µF
6.Hard
P = 40 kWQ1​S1​φ1​QC​

A single-phase load takes 40 kW at a power factor of 0.75 lagging from a 400 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the reactive power QC the capacitor must supply.

P = 40 kWpf1 = 0.75pf2 = 0.9V = 400 Vf = 50 Hz
QC = kvar

Answer key

  1. 1. P = 3680 W
  2. 2. cos φ = 0.7507
  3. 3. I = 39.5 A
  4. 4. Q = 14.11 kvar
  5. 5. C = 132.6 µF
  6. 6. QC = 15.9 kvar

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