Why Do Voltage and Current Phase Shift in LC Circuits?

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Discussion Overview

The discussion centers on the phase shift between voltage and current in LC circuits, exploring the physical justifications and underlying mechanisms that lead to this phenomenon. Participants examine the sinusoidal nature of voltage and current, the role of energy transfer between electric and magnetic fields, and the implications of these relationships in the context of circuit behavior.

Discussion Character

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

Main Points Raised

  • One participant asks for a physical justification of the 90-degree phase shift between voltage and current in LC circuits.
  • Another participant suggests that energy transfer between the electric field of the capacitor and the magnetic field of the inductor accounts for the phase shift, noting that when one is at a maximum or minimum, the other is zero.
  • A different viewpoint explains that in a capacitor, the sinusoidal voltage leads to a sinusoidal variation in charge concentration on the plates, which in turn affects the flow of electrons (current), resulting in a phase difference where current is zero when voltage is at its maximum.
  • One participant succinctly defines current as the movement of electrons and voltage as the power difference between two points.
  • In the context of inductors, a participant describes how the voltage across a solenoid is related to the rate of change of the magnetic field, which is directly tied to the current, leading to a 90-degree phase difference as well.
  • Another participant introduces the concept of energy conservation in LC circuits, stating that the energy stored in the capacitor and inductor must remain constant, which mathematically supports the phase relationship between voltage and current.

Areas of Agreement / Disagreement

Participants express various viewpoints on the mechanisms behind the phase shift, with some focusing on energy transfer and others on mathematical relationships. There is no consensus on a singular explanation, as multiple models and interpretations are presented.

Contextual Notes

Participants discuss the implications of sinusoidal functions and their derivatives in relation to phase shifts, but do not resolve the complexities of constants and signs in their arguments.

DirectCurrent
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How to physically justify it??

When current passes through a capacitor/inductor, the voltage and current are sinusoidal... mean voltage and current make an angle of 90 degrees.. what is the physical justification of this concept?? what actually happens inside a circuit?

Thanks in advance :-)
 
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What actually happens is that energy is transferred from the electric field of the capacitor to the magnetic field of the inductor. So when one is a maximum or a minimum the other is 0. This corresponds to a phase shift of 90º.
 


Assume that you enforce a sinusoidal voltage across a circuit consisting of just a capacitor. So the voltage difference between the capacitor plates is by definition sinusoidal. This must be consistent with the strength of the actual electric field between the plates in the cap. But for this electric field to exist, charges will have to have collected on the plates to create this field. The streng of this field is proportional to the amount of charges on the plates. Thus the amount of charges on the plates will have to vary in phase with the sinusoidal voltage.

So the concentration of the charges on the plates are sinusoidally time-dependent. How must the flow of electrons be to account for this? If the concentration of charges on the plates vary sinusoidally, then also the flow of electrons must do this (current).

To explain the phase difference: when the voltage is at its maximum, its rate of change is zero. Thus the flow of electrons must be zero at this time. Thus the current vanishes, and must be exactly 90degrees out of phase with the voltage.

Torquil
 


current: movement of electrons (sinusoidal).
voltage: power differernce between 2 point.
 


In the case of the inductor, the laws of electromagnetics tells you that the voltage difference across a solenoid can be found from the rate of change of the magnetic field inside the solenoid. The magnetic field inside the solenoid is directly related to the current going through the wire. Thus the potential difference can be found by differentiating the current.

The derivative of e.g. sin(wt) is w*cos(wt), or w*sin(wt+90degrees)

so you get a 90 degree phase difference also in this case.

In both these cases one shoud of course worry about constants and signs.

Torquil
 


Energy conservation requires that the energy stored in a capacitor-inductor (LC) circuit is a constant at all times. So ½CV2 + ½LI2 = constant. If voltage is sine-like, and current is cosine-like (90 degrees apart), then

½CV02 sine2(ωt) + ½LI02 cos2(ωt) = constant for all t.

A mathematical identity is cos2(ωt) + sin2(ωt) = 1, so ½CV02 = ½LI02

Bob S
 
Last edited:

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