How to physically justify it?

1. Jan 29, 2010

DirectCurrent

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????

2. Jan 29, 2010

Staff: Mentor

Re: How to physically justify it??

What actually happens is that energy is transfered 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.

3. Jan 29, 2010

torquil

Re: How to physically justify it??

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

4. Jan 29, 2010

Rajini

Re: How to physically justify it??

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

5. Jan 29, 2010

torquil

Re: How to physically justify it??

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

6. Jan 29, 2010

Bob S

Re: How to physically justify it??

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: Jan 29, 2010