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, 9.5 A and 1748 W. Find the reactive power Q taken by the load.

V = 230 VI = 9.5 AP = 1748 W

Q = var

2.Easy

A single-phase load draws 12 A (rms) from a 120 V (rms) supply at a power factor of 0.9 lagging. Find the real power P it takes.

V = 120 VI = 12 Apf = cos φ = 0.9

P = W

3.Medium

A load with impedance Z = 5 + j12 Ω is connected to a 120 V (rms) single-phase supply. Find the real power P it absorbs.

V = 120 VZ = 5 + j12 Ω

P = W

4.Medium

Two loads are connected in parallel to a 240 V single-phase supply: a 28 kW load at a power factor of 0.75 lagging and a 6 kW heater (unity power factor). Find the total current I drawn from the supply.

V = 240 VP₁ = 28 kW, pf₁ = 0.75 laggingP₂ = 6 kW, pf₂ = 1

I = A

5.Hard

A 120 V (rms), 1000 Hz source has an internal impedance Z_s = 10 + j20 Ω. The load impedance Z_L can be chosen freely. The load for maximum power is built from a resistor in series with a capacitor. Find the capacitance C.

V_s = 120 V (rms)f = 1000 HzZ_s = 10 + j20 Ω

C = µF

6.Hard

A single-phase load takes 10 kW at a power factor of 0.6 lagging from a 240 V, 60 Hz supply. A 100 µF capacitor is connected in parallel with the load. Find the new line current I.

P = 10 kWpf₁ = 0.6V = 240 Vf = 60 HzC = 100 µF

I = A

Answer key

1. Q = 1311 var
2. P = 1296 W
3. P = 426 W
4. I = 175.1 A
5. C = 7.958 µF
6. I = 62.44 A

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