How Does Resonance Affect Current and Impedance in a Parallel Circuit?

[FizixFreak]

why is the current minimum in a parallel resonance circuit and how is the impedence calculated in these circuits and can someone please explain this statement ''at reasonance the branch currents (current through inductor and capacitor)may be much larger than the source current''HOW can that happen (i have a hunch that they cancel each other) so we can say they might be greater than the source current but how can current be established in a crcuit which is greater than the source current it self? i know its a lot to ask but i m quite confused about all this stuff

 

[bjacoby]

why is the current minimum in a parallel resonance circuit and how is the impedence calculated in these circuits and can someone please explain this statement ''at reasonance the branch currents (current through inductor and capacitor)may be much larger than the source current''HOW can that happen (i have a hunch that they cancel each other) so we can say they might be greater than the source current but how can current be established in a crcuit which is greater than the source current it self? i know its a lot to ask but i m quite confused about all this stuff

The calculation of the impedance of a resonant parallel RLC circuit is rather complex involving imaginary numbers and would be difficult to explain here. The reason the branch currents are larger than than the input current is that energy is flowing back and forth from the capacitor to the inductor and back. Since that energy builds up over time it adds a tiny piece of the source energy with each cycle. And thus with enough cycles the stored energy (that is represented by the current surging back and forth) is greater than the source current.

Think of it this way. You have a large heavy pendulum. To get it swinging you tap on it repeatedly with a tiny hammer. If you've got the frequency of your taps right the pendulum will swing higher and higher with each tap. Eventually you have this huge bob swinging back and forth with much more energy than you had in anyone tap.

OK?

 

[FizixFreak]

mmmmmmmmmmmm welll here is another one

in a parallel resonance circuit is the resistive resistance also connected parallel to the other components??
what if it is in series

 

[Dale]

In an ideal parallel RLC circuit all of the elements are connected in parallel. The bulk of the current can still oscillate between the inductor and the capacitor, but each cycle a portion of the energy gets dissipated in the resistor. It essentially turns it from a simple harmonic oscillator to a damped harmonic oscillator.

 

[FizixFreak]

why does not the same happens in series resonance circuit

 

[FizixFreak]

In an ideal parallel RLC circuit all of the elements are connected in parallel. The bulk of the current can still oscillate between the inductor and the capacitor, but each cycle a portion of the energy gets dissipated in the resistor. It essentially turns it from a simple harmonic oscillator to a damped harmonic oscillator.

why does not the same happens in series resonance circuit??

 

[Dale]

It does.

 

[FizixFreak]

It does.

so how can current be maximum at resonance frequency in a series resonance circuit ??

 

[Dale]

so how can current be maximum at resonance frequency in a series resonance circuit ?

Here is the Hyperphysics page on series RLC circuits:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html

That is a good place to start, but you probably should at a minimum follow the link to impedance and learn a little about impedance. It turns out, in a series RLC circuit, that the impedance is minimum at the resonant frequency, which (by Ohm's law) means that the current is maximized for a given rms voltage.

??

I don't think that is quite enough question marks You probably need even more otherwise I might accidentally think that you are making statements instead of asking a question. Luckily, I figured it out in this case.

 

[FizixFreak]

Here is the Hyperphysics page on series RLC circuits:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html

That is a good place to start, but you probably should at a minimum follow the link to impedance and learn a little about impedance. It turns out, in a series RLC circuit, that the impedance is minimum at the resonant frequency, which (by Ohm's law) means that the current is maximized for a given rms voltage.

I don't think that is quite enough question marks You probably need even more otherwise I might accidentally think that you are making statements instead of asking a question. Luckily, I figured it out in this case.

sorry for not explaining my self but if the same thing happens in both series and parallel resonance circuit (current keeps bouncing back from capacitor to inductor an so on ) how can current be maximum in one condition (series ) and minimum in other (parallel)??(are these enough?)

 

[Dale]

sorry for not explaining my self but if the same thing happens in both series and parallel resonance circuit (current keeps bouncing back from capacitor to inductor an so on ) how can current be maximum in one condition (series ) and minimum in other (parallel)??(are these enough?)

It all depends where you measure the currents and voltages. In the series RLC circuit all of the elements share the same current, but each element has a different voltage across it. In the parallel RLC circuit all of the elements have the same voltage across them, but each element has its own current. In both the series and parallel arrangements the current through e.g. the capacitor is maximum at resonance, however in the series arrangement that is the same as the current through the resistor, but in the parallel arrangement it is not the same. In fact, in the parallel arrangement the current through the capacitor is almost exactly the opposite of the current through the inductor, so even though the current through those two elements is maximum at resonance the current through the source is minimum.

 

[FizixFreak]

dude if i m not wasting your time and since you are online why not help me out right now!

 

[Dale]

I would be glad to help, as always.

 

[FizixFreak]

It all depends where you measure the currents and voltages. In the series RLC circuit all of the elements share the same current, but each element has a different voltage across it. In the parallel RLC circuit all of the elements have the same voltage across them, but each element has its own current. In both the series and parallel arrangements the current through e.g. the capacitor is maximum at resonance, however in the series arrangement that is the same as the current through the resistor, but in the parallel arrangement it is not the same. In fact, in the parallel arrangement the current through the capacitor is almost exactly the opposite of the current through the inductor, so even though the current through those two elements is maximum at resonance the current through the source is minimum.

so basically in parrallel resonance circuit the current is minimum because the current through the inductor and the capacitor are opposite one leads other lags right but even in series resonance circuit the current through inductor and capacitor out of phase(by 90 degrees) so why is not current minimum for that circuit

 

[Dale]

even in series resonance circuit the current through inductor and capacitor out of phase(by 90 degrees) so why is not current minimum for that circuit

No, in series resonant circuit the current through the inductor and capacitor are the same (including in phase). It is the voltages that are out of phase.

 

[FizixFreak]

No, in series resonant circuit the current through the inductor and capacitor are the same (including in phase). It is the voltages that are out of phase.

but as far as i now in a series resonance circuit the current throgh capacitor is maximum when the current through inductor is minimum (am i wrong?) which means that they are out of phase because when current passes though inductor at that time the capacitor is storing charges on its end which means that the current across the capacitor is zero or minimum (i am definately missing something here)

 

[Dale]

but as far as i now in a series resonance circuit the current throgh capacitor is maximum when the current through inductor is minimum (am i wrong?)

Yes, you are wrong. By definition two circuit elements which are in series must always have the exact same current through them. Similarly, by definition two circuit elements which are in parallel must always have the exact same voltage across them.

 

[FizixFreak]

Yes, you are wrong. By definition two circuit elements which are in series must always have the exact same current through them. Similarly, by definition two circuit elements which are in parallel must always have the exact same voltage across them.

(1)the current cancels out only in parrallel resonance circiut
(2)voltage cancels out in series resonance circuit
rigth ?
but since the current through capacitor leads the voltage and the current through the inductor lags the voltage by vector diagram we can see that these current are not in phase how can they be in phase in any circuit?

 

[Dale]

Do you know the idea of complex impedance? The rest of the post will assume that you do, but if not then we can discuss that more fully.

Let's say that you have a series RLC circuit driven by an AC voltage source V cos(wt). Now, the complex impedances are:
Zr=R
Zl=jwL
Zc=1/(jwC)

so since series impedances add the total impedance is Z=R+jwL+1/(jwC) and so the current is I=V/(R+jwL+jwC). Now, by Ohms law we can obtain the voltage across each circuit element:
Vr = RV/(R+jwL+jwC)
Vl = jwLV/(R+jwL+jwC)
Vc = V/(jwC)(R+jwL+jwC)

Now, if we are specifically operating at the frequency w=1/sqrt(LC) then we find the following simplifications:
Zr=R
Zl=j sqrt(L/C)
Zc=-j sqrt(L/C)

The total impedance is then Z=R and so the current is I=V/R. Then by Ohms law the voltage across each circuit element is:
Vr=RV/R=V
Vl=j sqrt(L/c) V/R
Vc=-j sqrt(L/c) V/R

So, the voltage in the inductor leads the current by 90º, and the voltage in the capacitor lags the current by 90°, which means that the voltage in the inductor is 180º out of phase with the voltage in the capacitor. That is how they cancel each other out.

 

[FizixFreak]

Do you know the idea of complex impedance? The rest of the post will assume that you do, but if not then we can discuss that more fully.

Let's say that you have a series RLC circuit driven by an AC voltage source V cos(wt). Now, the complex impedances are:
Zr=R
Zl=jwL
Zc=1/(jwC)

so since series impedances add the total impedance is Z=R+jwL+1/(jwC) and so the current is I=V/(R+jwL+jwC). Now, by Ohms law we can obtain the voltage across each circuit element:
Vr = RV/(R+jwL+jwC)
Vl = jwLV/(R+jwL+jwC)
Vc = V/(jwC)(R+jwL+jwC)

Now, if we are specifically operating at the frequency w=1/sqrt(LC) then we find the following simplifications:
Zr=R
Zl=j sqrt(L/C)
Zc=-j sqrt(L/C)

The total impedance is then Z=R and so the current is I=V/R. Then by Ohms law the voltage across each circuit element is:
Vr=RV/R=V
Vl=j sqrt(L/c) V/R
Vc=-j sqrt(L/c) V/R

So, the voltage in the inductor leads the current by 90º, and the voltage in the capacitor lags the current by 90°, which means that the voltage in the inductor is 180º out of phase with the voltage in the capacitor. That is how they cancel each other out.

actually my question is quite hypothetical (i m familiar with this calculation )
but is not there a theoratical explanation to this stuf (i mean like with the help of an analogy or some thing)

 

[Dale]

If you are familiar with the calculation then what more is there? You can clearly see that the complex impedance is a minimum at the resonant frequency. I don't know what more you want. You have already been given analogy, theory, and math; all that remains is practice. I think you just need to work some circuit problems for yourself.

 

[Dale]

since the current through capacitor leads the voltage and the current through the inductor lags the voltage by vector diagram we can see that these current are not in phase how can they be in phase in any circuit?

Btw, just going back through this I noticed this error. In a series circuit the currents are the same, by definition, and therefore as you mentioned the voltages are 180º out of phase, never in phase. Resonance occurs when they are also equal in amplitude. In a parallel circuit the voltages are the same, by definition, and as therefore as you mentioned the currents are 180º out of phase, never in phase. Again, resonance occurs when they are also equal in amplitude.