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 240 V, 8 A and 1728 W. Find the reactive power Q taken by the load.

V = 240 VI = 8 AP = 1728 W

Q = var

2.Easy

A voltmeter, an ammeter and a wattmeter connected to a single-phase inductive load read 120 V, 20 A and 2040 W. Find the power factor cos φ of the load.

V = 120 VI = 20 AP = 2040 W

cos φ =

3.Medium

An inductive load takes 7 A and 630 W from a 120 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 120 VI = 7 AP = 630 W

R = Ω

4.Medium

A load with impedance Z = 12 + j9 Ω is connected to a 120 V (rms) single-phase supply. Find the real power P it absorbs.

V = 120 VZ = 12 + j9 Ω

P = W

5.Hard

A single-phase load takes 50 kW at a power factor of 0.7 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the capacitance C needed.

P = 50 kWpf₁ = 0.7pf₂ = 0.95V = 230 Vf = 50 Hz

C = µF

6.Hard

A single-phase load takes 25 kW at a power factor of 0.65 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.95. Find the reactive power Q_C the capacitor must supply.

P = 25 kWpf₁ = 0.65pf₂ = 0.95V = 230 Vf = 50 Hz

Q_C = kvar

Answer key

1. Q = 836.9 var
2. cos φ = 0.85
3. R = 12.86 Ω
4. P = 768 W
5. C = 2081 µF
6. Q_C = 21.01 kvar

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