Energy of Inductors in AC Circuit

[Ibraheem]

Hello,

In my textbook, it says that if we have a pure inductor connected to an AC source, the average power is zero. It explains that this is because the energy is used to create a magnetic field for the inductor and then it is extracted to the AC source.
So how is it possible for the inductor to extract the energy to the AC source and at what part of the cycle does this happen?

 

[drvrm]

So how is it possible for the inductor to extract the energy to the AC source and at what part of the cycle does this happen?

An inductor, also called a coil or reactor, is a passive two-terminal electrical part which resists changes in current passing through it.

It consists of a conductor such as a wire, usually wound into a coil.
Energy is stored in a field (magnetic) generated by the coil as long as current flows.
When the current flowing through an inductor changes with time , the time-varying magnetic field induces a voltage in the conductor working on Farady's law of induction .
According to Lenz's law the direction of induced E.M.F. is always such that it opposes the change in current that created it.

As a result, inductors always oppose a change in current but this is different from a resistance in usual parlance.

if we have a pure inductor connected to an AC source, the average power is zero.

Neglecting losses, the energy (measured in joules, in SI) stored by an inductor is equal to the amount of work required to establish the current through the inductor, and therefore the magnetic field. This is given by:

where L is inductance and I is the current through the inductor.
An inductor’s opposition to change in current translates to an opposition to alternating current in general, which is by definition always changing in instantaneous magnitude and direction. This opposition to alternating current is similar to resistance, but different in that it always results in a phase shift between current and voltage, and it dissipates zero power. Because of the differences, it has a different name: reactance.

for details see https://en.wikipedia.org/wiki/Inductor#Stored_energy

 

[Dale]

at what part of the cycle does this happen?

Whenever current is going into the terminal at the higher voltage then energy is flowing into the inductor. Whenever current is going out of the terminal at the higher voltage then energy is flowing out of the inductor.

 

[Ibraheem]

So does this mean the inductor returns its energy to the source only when it is inducing a current in the direction of the AC polarity?In other words, the inductor returns its energy to the source when the current induced is in the direction of the decreasing(not yet reversed) current in the circuit.
I understand how the energy from the AC source is used to create a magnetic field in the inductor, but I am having a hard time to visualize how the inductor returns the energy to the source.

 

[NascentOxygen]

Draw a pair of sinusoids, with one leading the other. This leading waveform can represent the voltage from the source applied to the inductor, the other being the current.

There are intervals during the cycle where the source voltage is positive yet the current drawn from the source is negative. The product of these instantaneous values is power, and this negative power indicates power returning into the source. These intervals are precisely matched at other intervals by a positive i(t).v(t) product which indicates where power is being delivered to the inductor.

You can draw the power waveform by plotting lots of points, each being the instantaneous current value multiplied by the corresponding instantaneous voltage value. Over one cycle, the power averages to zero: confirming there is no power loss in a pure inductance.

 

[Ibraheem]

But how is this energy returned?In other words, where does it exactly go when the magnetic field collapses? I know it was first used to set up a magnetic field, but is it used to push charge in the wire when the power is negative?

 

[Dale]

where does it exactly go

It goes into whatever the inductor is attached to. If it is attached to a resistor then it will go out as thermal energy. If it is attached to a capacitor then it will go into the electric field. Etc.

 

[larsa]

It goes into whatever the inductor is attached to. If it is attached to a resistor then it will go out as thermal energy. If it is attached to a capacitor then it will go into the electric field. Etc.

If it is attached to a generator the energy goes to the magnetic field of the generator's stator?

 

[Dale]

Yes. Depending on the motor design it could also be the rotor. And then of course eventually to mechanical work.

 

[anorlunda]

https://www.physicsforums.com/insights/ac-power-analysis-part-1-basics/

That article discusses this question.