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

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 230 V, 11 A and 2024 W. Find the power factor cos φ of the load.

V = 230 VI = 11 AP = 2024 W

cos φ =

2.Easy

A single-phase load draws 12 A (rms) from a 120 V (rms) supply at a power factor of 0.65 lagging. Find the real power P it takes.

V = 120 VI = 12 Apf = cos φ = 0.65

P = W

3.Medium

A load with impedance Z = 5 + j12 Ω is connected to a 230 V (rms) single-phase supply. Find the apparent power S.

V = 230 VZ = 5 + j12 Ω

S = VA

4.Medium

Two loads are connected in parallel to a 400 V single-phase supply: a 2 kW load at a power factor of 0.75 lagging and a 6 kW load at a power factor of 0.95 lagging. Find the overall power factor cos φ seen by the supply.

V = 400 VP₁ = 2 kW, pf₁ = 0.75 laggingP₂ = 6 kW, pf₂ = 0.95 lagging

cos φ =

5.Hard

A single-phase load takes 5 kW at a power factor of 0.7 lagging from a 240 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the new line current I_new.

P = 5 kWpf₁ = 0.7pf₂ = 0.95V = 240 Vf = 60 Hz

I_new = A

6.Hard

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 0.98. Find the reactive power Q_C the capacitor must supply.

P = 20 kWpf₁ = 0.7pf₂ = 0.98V = 240 Vf = 50 Hz

Q_C = kvar

Answer key

1. cos φ = 0.8
2. P = 936 W
3. S = 4069 VA
4. cos φ = 0.9061
5. I_new = 21.93 A
6. Q_C = 16.34 kvar

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