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 single-phase load draws 17 A (rms) from a 230 V (rms) supply at a power factor of 0.8 lagging. Find the reactive power Q it takes.

V = 230 VI = 17 Apf = cos φ = 0.8

Q = var

2.Easy

A single-phase load draws 20 A (rms) from a 240 V (rms) supply at a power factor of 0.9 lagging. Find the real power P it takes.

V = 240 VI = 20 Apf = cos φ = 0.9

P = W

3.Medium

An inductive load takes 16.5 A and 1898 W from a 230 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 230 VI = 16.5 AP = 1898 W

R = Ω

4.Medium

An inductive load takes 4 A and 552 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 = 4 AP = 552 W

X = Ω

5.Hard

A single-phase load takes 5 kW at a power factor of 0.75 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the reactive power Q_C the capacitor must supply.

P = 5 kWpf₁ = 0.75pf₂ = 0.9V = 230 Vf = 50 Hz

Q_C = kvar

6.Hard

A single-phase load takes 40 kW at a power factor of 0.8 lagging from a 400 V, 60 Hz supply. A capacitor connected in parallel raises the power factor to 0.92. Find the new line current I_new.

P = 40 kWpf₁ = 0.8pf₂ = 0.92V = 400 Vf = 60 Hz

I_new = A

Answer key

1. Q = 2346 var
2. P = 4320 W
3. R = 6.972 Ω
4. X = 46 Ω
5. Q_C = 1.988 kvar
6. I_new = 108.7 A

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