IntermediateTopic 42 of 106Electrical Engineering

Power in AC circuits

Real power P, reactive power Q and apparent power S relate by S²=P²+Q².

In depth

Real power P=VI cosφ (W), reactive Q=VI sinφ (VAr) and apparent S=VI (VA) with S²=P²+Q². Complex power S=VI*. Utilities bill demand in kVA because reactive current loads the system without doing useful work.

Key points

  • Power triangle
  • Instantaneous power pulses at 2f
  • Only R dissipates average power
Example

230 V and 10 A at 30° gives P=1.99 kW and Q=1.15 kVAr.

Why it matters

Real, reactive and apparent power describe how AC power is used, stored and delivered, which determines equipment ratings.

Where this is used

  • Sizing a transformer kVA for a building with motor loads.
  • Calculating the reactive power a capacitor must supply.
  • Choosing a generator rating for a mixed load of heaters and motors.

Frequently asked questions

What is Power in AC circuits?

Real power P, reactive power Q and apparent power S relate by S²=P²+Q².

Why is it important to understand power in AC circuits?

Real, reactive and apparent power describe how AC power is used, stored and delivered, which determines equipment ratings.

What is the unit of apparent power?

The volt-ampere, shown as VA or kVA, which is the product of RMS voltage and RMS current.

Why do transformers have kVA ratings?

Transformer losses depend on current and voltage, not on the power factor of the load, so they are rated in apparent power.

How is Power in AC circuits used in practice?

Typical applications include sizing a transformer kVA for a building with motor loads, calculating the reactive power a capacitor must supply and choosing a generator rating for a mixed load of heaters and motors.

What should I learn before Power in AC circuits?

Study "Reactance" first (topic 41 of 106 in Electrical Engineering). It covers the groundwork this topic builds on.

What are the key points of Power in AC circuits?

Power triangle. Instantaneous power pulses at 2f. Only R dissipates average power.

Can you give an example of Power in AC circuits?

230 V and 10 A at 30° gives P=1.99 kW and Q=1.15 kVAr.

What comes after Power in AC circuits?

The next topic is "Power factor", which builds directly on this one.

How difficult is Power in AC circuits?

It is classed as Intermediate in Electrical Engineering (topic 42 of 106). It is an intermediate topic. Work through the beginner topics in Electrical Engineering first.

Learning path

Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.

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