# Reactive power in AC circuit

What is meant by reactive power in AC circuits? Power is joules per second.

Real power is the energy dissipated in the resistor per second.

What is meant by the reactive power? Does this mean the energy being stored in capacitor and inductor per second, or does it mean the stored energy supplied per second by the inductor or capacitor.

If we have a voltage source connect with an RLC network and after some time the inductor and capacitor are suddenly detached from the network and then they are supplied to another resistor with diffent value without voltage source then of course they will supply the energy at a new rate to the new resistance depending upon value the resistance. Will this not make the value of stored energy per second different from the value of energy supplied per second? Doesn't that give two different values of reactive power? Doesn't this mean that the reactive power is now changed for the same capacitor and inductor?

• Hmmm are you sure this one isn't a duplicate?
– K H
Mar 31, 2021 at 7:52
• @Transistor, Many thanks for your advice. So I will delete my comments and try to write up an answer later. Cheers. Mar 31, 2021 at 13:41

What is meant by reactive power in AC circuits.

• Real power is $$\V\cdot I\cdot \cos(\theta)\$$
• Reactive power is $$\V\cdot I\cdot\sin(\theta)\$$
• Apparent power is $$\V\cdot I\$$ (derived from the above using Pythagoras) Picture from here

Capacitors and Inductors are Reactors and account for the reactive power in an AC circuit. When you measure the current and voltage in an AC circuit, you measure what is called Apparent Power, which will appear to be greater than the actual True Power being used in the circuit if the circuit has reactors in it. They store and release energy, causing current to flow in the process even though the Reactive Power isn't being used and contributing to the "Power" you "see". To recognise the difference between the energy being stored and being used, we refer to True Power in W(watts), Reactive Power in VAR (volt-amps reactive) and Apparent Power in VA (volt-amps).

The Apparent Power is not simply the sum of the True Power and the Reactive Power. Instead it's a Pythagorean relationship where the Apparent power is the long side of a square triangle, the True Power is the horizontal line and the Reactive Power is the vertical line. You can apply trigonometric rules and the Pythagorean Theorem to calculate values on different sides of the triangle from your known values.

## Reactive power

"In ac circuits, energy flows into and out of energy storage elements (inductances and capacitances). For example, when the voltage magnitude across a capacitance is increasing, energy flows into it, and when the voltage magnitude decreases, energy flows out. Similarly, energy flows into an inductance when the current flowing through it increases in magnitude. Although instantaneous power can be very large, the net energy transfered per cycle is zero for either an ideal capacitance or inductance.

When a capacitance and an inductance are in parallel energy flows into one, while it flows out of the other. Thus, the power of a capacitance tends to cancel that of an inductance at each instant in time.

The peak instantaneous power associated with the energy storage elements contained in a general load is called reactive power and is given by $$Q=V_{RMS}I_{RMS}\cdot \sin(\theta_v-\theta_i)$$

The physical units of reactive power are watts. However, to emphasize the fact that $$\Q\$$ does not represent the flow of net energy, its units are usually given as Volt Amperes Reactive (VARs)."

## Importance of reactive power

"Even though no average power is consumed by a pure energy-storage element, reactive power is still of concern to power-system engineers because transmission lines, transformers, fuses, and other elements must be capacble of withstanding the current associated with reactive power. It is possible to have loads composed of energy-storage elements that draw large currents requiring heavy-duty wiring, even though little average power is consumed. Therefore, electric-power companies charge their industrial customers for reactive power as well as for total energy delivered."

## Source

Electrical Engineering Principles and Applications by Allan R. Hambley

• It might be useful to clarify the significance of the sign of reactive power. If a load whose reactive power is positive is connected in parallel with one whose reactive power is negative, one load may use energy it stored during part of each cycle to feed power to the other load which will then store it for later return back to the first load. Mar 31, 2021 at 20:53
• Carl - Thanks. Do you have a link? || That indicates that the answer is wholly from the cited text. I'm not meaning to be nitpicking (or a pain :-) :-( ) and you can leave it as is or change it as desired but where the material is entirely quoted then stating this at the top gives a clearer indication. Apr 1, 2021 at 11:57
• A source is all that is necessary if it's coming from off the web Apr 2, 2021 at 19:13

Reactive power is a concept that comes out in AC circuits where the voltage or current sources have a sine wave shape with a certain fixed frequency f.

Picture this circuit: a sine wave voltage source V that charges and discharges a capacitor C. They are in parallel. Vc(t) = V * sin (2 * pi * f * t)


V and f are fixed.

Look at this picture from Wikipedia: Initially the capacitor is discharged.

The current flows from the source to the capacitor. We like that.

When Vc reaches its maximum V, the capacitor GIVES BACK the current to the source.

The bad thing for the voltage source is that it is receiving current from the capacitor while V is still positive. When V is positive, the voltage source is supposed to push power to the load.

Reactive power is the power that the capacitor C returns back to the voltage source.


Power is the blu line in the picture.

It changes in time.

If you take its integrals in the 90-180 and 270-360 intervals you have the reactive power over the period T = 1/f

What is meant by the reactive power? Does this mean the energy being stored in capacitor and inductor per second, or does it mean the stored energy supplied per second by the inductor or capacitor.

"Real power", "apparent power" and "reactive power" are all concepts derived from somthing more fundamental in circuit analysis: instantaneous power, which is simply equals to V*I.

As the name implies, instantaneous power is calculated at an instant, and as such, can change as time progresses. This makes it unwieldy: even in a resistor, it changes accordingly to the voltage applied. Because of that, is it impossible to describe instantaneous power with a single number: it has to be a function of time.

In the context of steady state AC circuits, however, it is convenient to average things out in a cycle. This is how we get "real power": it is simply the average power in a cycle. In this context, if I say a resistor dissipates 1W, this does not mean that the resistor's instantaneous power is 1W all the time: it sometimes is 0W (at zero voltage), and sometimes is 2W (at max positive or max negative voltage), averaging out to 1W. (note that the instantaneous value will never be negative)

Apparent power and reactive power are other derived quantities that only apply in linear steady state AC circuits: they measure the power flow in elements caused by currents that are offset by 90 degrees from the voltage wave. Such power flow averages out to zero, but instantaneous power is not always zero: it goes from positive (absorbing energy) to negative (providing energy). An inductor that sinusoidally goes from providing 1W to absorbing 1W is said to consume 1VAR of power, and a capacitor whose instantaneous power is the opposite of such inductor (that is, absorbing 1W when the inductor provides 1W, and vice-versa) is said to produce 1VAR.

Question The OP asks the following questions:

1. What is meant by reactive power in AC circuits?

2. Real power is the the energy dissipated in the resistor per second. Then what is meant by the reactive power?

2.1 Does this mean the energy being stored in capacitor and inductor per second?

2.2 Or does it mean the stored energy supplied per second by the inductor or capacitor?

3. If we have a voltage source connected with RLC network and after some time the inductor and capacitor are suddenly detached from the network and then they are supplied to another resistor with different value without voltage source then of course they will supply the energy at a new rate to the new resistance depending upon value the resistance.

3.1 Will this not make the value of stored energy per second different from the value of energy supplied per second?

3.2 And doesn't that give the two different values of reactive power?

3.3 Doesn't this mean that the reactive power is now changed for the same capacitor and inductor?

Part 1 - A summary of the OP's questions

The OP is basically asking the following:

1. How "Reactive Power" is different from "Real Power"?

1.1 About "Real Power" - Is it true that "Real power" is the electrical power which transforms/converts/dissipates electrical energy into to a lower form heat energy absorbed by a resistor, which becomes heated, and then "transfers" its absorbed heat energy to its surrounding air which becomes warmer. In other words, heat energy is not stored but gone forever into the Universe.

1.2 About "Reactive Power" - Is it true that "Reactive Power" is the electrical power which converts electrical energy to build up (a) a "magnetic field" around an current flowing inductor, and/or (b) an electric field/potential inside a charged up capacitor?

Now, is "Inductive/Magnetic Field Energy" and/or "Capacitive/Electric field energy" never get transformed to a lower/inferior energy. But can they be transformed back to electrical energy? (Note 1)

Note 1 - This answer confines to oversimplified RLC power/energy. Therefore, induction motor which indeed can convert magnetic field power/energy to mechanical power/energy is not considered/discussed.

Part 2 - The answer

2.1 What is reacting power?

/ to continue, ...

2.2 What happens in the thought experiment of "Inductor and capacitor with stored energy disconnect from current resistor and connect to another new resistor"?

/ to continue, ...

References

Appendices

Appendix A - Charging a capacitor and Inductor Transient  Appendix B - Energy stored in capacitor and inductor Appendix C - Reactive Energy Analogy • Please stop creating long posts, and keep the edits down to less than 5 Apr 1, 2021 at 21:14
• Thank you for your advice. Cheers. Apr 2, 2021 at 0:40
• This post (and its style) is being discussed on meta: Lengthy "blog style" attempts to answer - how to treat them? (or was a couple weeks ago) Apr 15, 2021 at 20:43