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
400 Vload9.5 kW, 3.5 kvarI = ?

A single-phase load connected to a 400 V supply takes 9.5 kW and 3.5 kvar. Find the current I drawn from the supply.

V = 400 VP = 9.5 kWQ = 3.5 kvar
I = A
2.Easy
400 Vload17 kW, 16.5 kvarI = ?

A single-phase load connected to a 400 V supply takes 17 kW and 16.5 kvar. Find the current I drawn from the supply.

V = 400 VP = 17 kWQ = 16.5 kvar
I = A
3.Medium
240 VR + jXP = 1512 W7 A

An inductive load takes 7 A and 1512 W from a 240 V (rms) single-phase supply. Model it as a resistance R in series with a reactance X. Find R.

V = 240 VI = 7 AP = 1512 W
R = Ω
4.Medium
P = 39 kWQSφ

A single-phase motor takes 39 kW at a power factor of 0.85 lagging from a 230 V supply. Find the line current I.

P = 39 kWpf = 0.85V = 230 V
I = A
5.Hard
P = 35 kWQ1​S1​φ1​QC​

A single-phase load takes 35 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 0.95. Find the reactive power QC the capacitor must supply.

P = 35 kWpf1 = 0.8pf2 = 0.95V = 400 Vf = 60 Hz
QC = kvar
6.Hard
230 V1000 HzRs​ = 2 ΩXs​ = j15 ΩZL​ = ?

A 230 V (rms), 1000 Hz source has an internal impedance Zs = 2 + j15 Ω. The load impedance ZL can be chosen freely. Find the maximum real power Pmax that can be delivered to the load.

Vs = 230 V (rms)f = 1000 HzZs = 2 + j15 Ω
Pmax = W

Answer key

  1. 1. I = 25.31 A
  2. 2. I = 59.23 A
  3. 3. R = 30.86 Ω
  4. 4. I = 199.5 A
  5. 5. QC = 14.75 kvar
  6. 6. Pmax = 6613 W

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