AC Power and Power Factor

Electrical Engineering · CHAPTER 3 / 5

Level: introductory undergraduate · Study session: 15–20 minutes including practice.

Learning outcome: Distinguish real, reactive and apparent power for sinusoidal loads.

Before you begin: Complete earlier chapters in this discipline; revise algebra and units as needed.

1. Understand the idea

For sinusoidal steady-state voltage and current, real power performs net work over a cycle. Reactive power represents oscillating energy exchange. Apparent power sizes equipment. The displacement power factor is cosφ; distorted waveforms require a broader definition using measured real power and RMS quantities.

2. Write the model

S = Vrms Irms; P = S cosφ; Q = S sinφ

Define the symbols from the worked case before substituting values. Keep units consistent, record the assumptions and round only after the calculation.

3. Follow a worked example

A single-phase 230 V load draws 10 A at power factor 0.8 lagging. S=2300 VA, P=1840 W and Q=1380 var. At the same real power, lower power factor requires more current.

4. Explore the model

Figure: calculated teaching cases; straight segments connect sampled points, not experimental observations. Read exact values below.

Illustrative scenario sweep — synthetic educational data
Power factor	P fixed (W)	Current at 230 V (A)
1	1840	8
0.8	1840	10
0.6	1840	13.333

Keep real power fixed and reduce power factor. Current rises, increasing I²R loss in an unchanged conductor.

5. Reproduce it yourself

Copy the input cases into Excel or a notebook and name each quantity and unit.
Recalculate each result from the stated equation or rule. For qualitative cases, explain the state or partition decision instead.
Change one input, predict the direction of change, then calculate again.
Write one sentence explaining where the model stops being valid.

6. Check your understanding

What is apparent power at 230 V and 5 A?

Reveal the answer and check your work

1150 VA.

Compare your result, units and reasoning. If they differ, return to the equation and test the worked case first.

7. Common mistake

Do not use the single-phase formula unchanged for a three-phase system.

Further study and academic note

Explore the discipline reference and further learning resources. This is an original IIMEEE introductory teaching note with synthetic examples; it is not a peer-reviewed research result or a professional design specification. Figures were constructed from the listed teaching cases. Resource links support further study and do not imply endorsement.