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 120 V, 8 A and 720 W. Find the power factor cos φ of the load.

V = 120 VI = 8 AP = 720 W

cos φ =

2.Easy

A single-phase load draws 4 A (rms) from a 120 V (rms) supply at a power factor of 0.6 lagging. Find the reactive power Q it takes.

V = 120 VI = 4 Apf = cos φ = 0.6

Q = var

3.Medium

An inductive load takes 12.5 A and 2012 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find X.

V = 230 VI = 12.5 AP = 2012 W

X = Ω

4.Medium

A load with impedance Z = 8 + j6 Ω is connected to a 120 V (rms) single-phase supply. Find the real power P it absorbs.

V = 120 VZ = 8 + j6 Ω

P = W

5.Hard

A single-phase load takes 15 kW at a power factor of 0.75 lagging from a 400 V, 60 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 = 15 kWpf₁ = 0.75pf₂ = 0.98V = 400 Vf = 60 Hz

Q_C = kvar

6.Hard

A 200 kVA single-phase transformer supplies a load of 44 kW at a power factor of 0.6 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

S_max = 200 kVAP₁ = 44 kWpf₁ = 0.6

ΔP = kW

Answer key

1. cos φ = 0.75
2. Q = 384 var
3. X = 13.14 Ω
4. P = 1152 W
5. Q_C = 10.18 kvar
6. ΔP = 147.2 kW

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