Energy in AC-Driven Purely Inductive/Capacitive Circuit

  • Context: Graduate 
  • Thread starter Thread starter modulus
  • Start date Start date
  • Tags Tags
    Circuit Energy
Click For Summary

Discussion Overview

The discussion revolves around the behavior of energy in AC-driven purely inductive and capacitive circuits, focusing on the implications of power factor and energy transfer. Participants explore theoretical concepts, analogies, and real-world applications, examining the nature of energy flow and losses in such circuits.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that in purely capacitive and inductive circuits, the power factor is zero due to a 90° phase difference, suggesting no power is transferred, yet questions how energy can build up given the continuous input from the AC source.
  • Another participant describes energy oscillating between the generator and the capacitor or inductor, likening it to a bicycle wheel that requires minimal power to maintain once in motion, while emphasizing that real-world resistance affects this ideal scenario.
  • A third participant challenges the relevance of ideal scenarios without resistance, arguing that real circuits must account for energy losses due to radiation and resistive components, advocating for a complete analysis of circuit behavior.
  • One participant expresses understanding of the energy input dynamics, comparing it to applying force to a slowing wheel, while acknowledging the importance of practical considerations in circuit design.
  • Another participant shares their experience with a coilgun project, highlighting the significant impact of resistance on energy transfer and circuit performance, while recognizing the theoretical nature of the current discussion.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of ideal versus real-world scenarios, with some advocating for theoretical exploration while others emphasize practical considerations. No consensus is reached regarding the implications of energy transfer in purely inductive or capacitive circuits.

Contextual Notes

Limitations include the assumption of ideal components without resistance, the dependence on theoretical models, and the unresolved nature of energy losses in practical applications.

modulus
Messages
127
Reaction score
3
The power losses in an AC-driven circuit depend not only upon the rms voltages and currents in the circuit, but also the power factor, cos\phi, where \phi is the phase difference between the current and the applied alternating voltage.
In purely capacitive and purely inductive circuits, the phase difference is 90°, and so, the power factor is:
cos(90°) = 0​
.
Which means there is no power transferred from the alternating voltage source to any part of the circuit.
But how is that possible? The alternating voltage produced by a dynamo (or nay other AC source), during every cycle involve new energy inputs (the rotating armature) every cycle. So, there should be an energy buildup somewhere...
The energy seen in the form of voltage in one direction can't go back to the ac source during the time the voltage decays, because then there would be a buildup of energy in the source - the energy that is returning to it during voltage decay, and the new energy that produces the voltage of the next half of the cycle.
There seems to be a contradiction...
 
Physics news on Phys.org
Energy will just slosh back and forth between the generator and the capacitor or inductor. Once 1/2CV2 or 1/2LI2 has been generated, the amount of mechanical power required to turn the generator will only be whatever is required to overcome parasitic loss. It will be like picking a bicycle wheel off the ground and giving it a spin: once the wheel is up to speed it takes almost zero power to keep it spinning.

When the ideal generator voltage drops during the AC cycle, the ideal C/L will feed all of the energy back to the generator. The generator will become an ideal motor, giving back the mechanical energy which was previously supplied. It will be like running the steam turbine or engine or whatever mechanical energy source with no load.

And of course in the real world the circulating current has to plow through the resistance of the circuit, which is why poor power factor is undesirable...it's current that's clogging up the wires, transformers and such without doing any useful work.
 
Last edited:
@modulus
There is little point in considering such 'ideal' situations because they lead to conclusions that have no relevance to real-life. You really have to include some resistance in your circuit or the scenario makes no sense. Remember that, in any case, if there are changing currents and voltages in any circuit, there will be a finite amount of energy radiated as EM waves. That, in itself, is equivalent to having a resistor in the circuit.
I think you just need to bite the bullet and use the equations in their complete form, including the resistive components. You can then investigate the limiting behaviour as the resistance approaches zero.
 
@RankineCycle
Ok...I get it! The bicycle wheel analogy really helped. From what I have understood, the AC generator will not input extra energy into the circuit periodically, it will do so as and when it is needed by the circuit. This is similar to how we would apply a force to the spinning wheel only when it begins to slow down. Please correct me if I'm wrong.
And I noticed this is your first post...so, welcome to Physics Forums! I really appreciate that you took the time to create an account to answer my question.
Thanks a bunch!

@sophiecentuar
Yes, of course. That is what I strive to do.
But I think that sort of analysis is more relevant and effective when you're trying to make something practically. This past month, I was working on a coilgun...and I realized how much different real-world situations can be. The inductor coil I was making had considerable resistance, and I had to carefully assess the effect of its internal resistance on the entire system.
But this post was meant for a theoretical discussion.
Though I completely agree with you, and understand you. :)
 

Similar threads

High School Antenna induction, oscillating circuit generating EM Waves
  • · Replies 6 ·
Replies
6
Views
2K
High School How can scalars like voltage, impedance, etc. be added like vectors?
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Facing issues in understanding a Purely Inductive Circuit
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Energy of Inductors in AC Circuit
  • · Replies 9 ·
Replies
9
Views
2K
Calculation of current in driven series RLC circuit
  • · Replies 8 ·
Replies
8
Views
3K
Alternator torque when connected to a phase-shifted AC source
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Understanding AC Circuits: Questions About Light Bulbs and Complex Impedance
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Boundary conditions for a purely inductive load in an AC circuit
  • · Replies 30 ·
2
Replies
30
Views
3K
Graduate Energy in AC Circuits: No Frequency Involved
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What is the relationship between voltage, electric potential, and power?
  • · Replies 1 ·
Replies
1
Views
2K