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Author Topic: Introduction to Resonance  (Read 23067 times)

Offline barbosi

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Re: Introduction to Resonance
« Reply #15 on: October 10, 2008, 09:43:32 PM »
There is something I'm missing. While all this stuff meets all common knowledge and I'm not going to argue about that, there are few formulas thought in schools that do not make any sense to me.

An example is here http://www.pronine.ca/lcf.htm and for your convenience I attach a screenshot.

So my trouble is to understand where is the impedance formula coming from?
And I'm sure it is pretty familiar to many.
Does anyone realises that the infinite impedance (at resonance) has the value of 31.6227... ohms? ??? >:( (see screenshot)

Maybe is just me sweeping under the rocks...

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Re: Introduction to Resonance
« Reply #15 on: October 10, 2008, 09:43:32 PM »

Offline AbbaRue

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Re: Introduction to Resonance
« Reply #16 on: October 10, 2008, 09:52:03 PM »
If I wanted to get 2 coils to resonate at alternated times and use the back emf of one to help energize the other.
How would I go about doing this?
Sort of a teeter toter effect.
I want to make a 2 cylinder electromagnetic piston engine.

Offline armagdn03

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Re: Introduction to Resonance
« Reply #17 on: October 10, 2008, 10:22:55 PM »
To awnser Barbosi

In a perfect world, there would be no losses in the components. Perfect inductors, and perfect capacitors would give infinite impedance in parallel configuration, and zero impedance in series. The calculation given for impedance is a closer aproximation to real life where we do not have perfect loss-less systems. You can see from the equation which components to use to get higher or lower impedances.

To awnser AbbaRue

Sorry, im not here to speculate on how to make certain devices, if you think about why whats happening is happening, you will find that that is not directly possible.

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Re: Introduction to Resonance
« Reply #17 on: October 10, 2008, 10:22:55 PM »
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Offline barbosi

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Re: Introduction to Resonance
« Reply #18 on: October 10, 2008, 10:47:41 PM »
The calculation given for impedance is a closer aproximation to real life where we do not have perfect loss-less systems.

Well this is a darn sloppy approximation. And the formula for impedance is flat out wrong if you pay attention to the parameters. While you may have for different values the same resonant frequency, the impedance varies like hell.

From the values on my screenshot you get frequency about 50kHz and Z abut 31 ohms/.
If you change to C=100uF and L=100nH you'll have the same frequency but Z=0.031 ohms  :-\ (which in no way approximates infinite).

That was all my point and I see almost nowhere that familiar formula, which was also kind of useless.
And I'm pretty sure was at the base of transmission lines theory, matching impedance stuff, etc.
But is OK, I'm not going to hog the thread with a pervert formula.  :-X

Offline armagdn03

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Re: Introduction to Resonance
« Reply #19 on: October 10, 2008, 11:42:41 PM »
HA HA HA  ;D
that rant cracked me up a bit,

I didnt actually check the acuracy of that formula, I cannot vouch for it. The one for finding resonant freq is correct though. But its true, you may have the same resonant freq with diferent sized caps and inductors, which will have different impedances. Impedance matching is important when optimising, for now though, this information is just meant to give the bigger picture, dont get bogged down with details. Find other calculators, find books, find articles, check formulas, go and learn!

And hey........dont just take one source and believe it! fact check! be a detective! I just like that calc because you could enter any 2 of 3 variables, didnt ever really use the impedance part, notice I didnt talk about calculating impedance....were not there yet.

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Re: Introduction to Resonance
« Reply #19 on: October 10, 2008, 11:42:41 PM »
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Offline Charlie_V

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Re: Introduction to Resonance
« Reply #20 on: October 11, 2008, 02:47:39 AM »
The impedance the formula gives is what they call the characteristic impedance.  It is correct but with respect to the objects at hand.  The idea behind this is if you want to transmit power from one circuit to the other, you want their Zo (characteristic impedance) to match, and you get maximum real power transfer.  The more the Zo of one circuit mismatches the other circuit, then the more energy will go back and forth between circuits - aka the more oscillations you will have. 

As an example, if you could put a variable capacitor in parallel to your house's breaker box (where the power comes in from the pole) and start changing the capacitance, at some point your house's Zo will match perfectly with the Zo of the transmission line, but if you keep changing it, you can get it to a point where they are greatly mismatched and nothing in your house will turn on.  But the standing waves on the transmission line won't last long because the power companies have instruments that watch for standing waves and kill them whenever they start. 

With Tesla coils you want your primary and secondary circuit to be as greatly mismatched as possible.  There are also tricks like using an extra coil to help reduce damping that occurs when the secondary is near the primary inductor.  But all this is fine and dandy, I'm interested on how an oscillating load is useful?  If it just oscillates there and doesn't power anything in your house, what is the use?  Maybe I'm missing something?

Offline gotoluc

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Re: Introduction to Resonance
« Reply #21 on: October 11, 2008, 07:14:45 AM »
Hi armagdn03,

I've been pulsing inductor for a while but always using square wave to trigger a transistor that pulses a DC source, since my Wavetek 234 has no real power output. On its own it can only light one LED at max output. I see that your signal generator is capable of lighting a 6 vdc flashlight bulb with sign wave. Can you or someone else please tell me what I have to do or get to be able to have a higher power output so I can do the same tests as you are doing.

Another thing I'm wondering about is, to achieve resonance in an inductor is it only possible to do it with a capacitor or is it possible to do it without one? I have noticed inductors without a capacitor have a certain frequency that the amplitude goes up. I have 2 air core inductors that at 1.64Mhz do this.

Thanks

Luc

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Re: Introduction to Resonance
« Reply #21 on: October 11, 2008, 07:14:45 AM »
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Offline amigo

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Re: Introduction to Resonance
« Reply #22 on: October 11, 2008, 04:19:54 PM »
Here's a page I liked that explains the impedance in relations to capacitors and inductors. I also like the two graphs of the resonance in relation to frequency and current at the bottom of the page, displaying the characteristics when LC are in series or parallel.

http://arts.ucsc.edu/EMS/Music/tech_background/Z/impedance.html

Also, regarding impedance, my understanding is that impedance is 0 at the resonance, not infinite as someone mentioned above. It has to be 0 because XL has to equal XC and in series circuit that happens when one goes to the other side of the = sign. In parallel circuit you are dividing by 0 (as XL = XC) so conditions are satisfied.

On that page right before the Transformer section it describes minimum current at resonance of parallel circuit due to two waves canceling out:

As the frequency rises, the inductor impedes, but the capacitor will take over. When the impedances of both match, you get no current flow. How is this possible?

It's because of the phase changes: the current through a capacitor is 90° ahead of the voltage, and the current through the inductor is 90° behind. When the circuit is in resonance, the two cancel out. In real circuits, series resistance tends to reduce the peaks. This is called damping, and the ratio of inductive reactance to resistance is known as Q (for quality factor).


@Charlie_V

You said that in Tesla coils, primary and secondary need to be mismatched as much as possible. Wouldn't that imply that the energy would be wasted in the primary trying to keep the oscillations going in the secondary which is out of tune?

Offline Charlie_V

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Re: Introduction to Resonance
« Reply #23 on: October 12, 2008, 12:51:43 AM »
Quote
Also, regarding impedance, my understanding is that impedance is 0 at the resonance, not infinite as someone mentioned above. It has to be 0 because XL has to equal XC and in series circuit that happens when one goes to the other side of the = sign. In parallel circuit you are dividing by 0 (as XL = XC) so conditions are satisfied.

On that page right before the Transformer section it describes minimum current at resonance of parallel circuit due to two waves canceling out:

As the frequency rises, the inductor impedes, but the capacitor will take over. When the impedances of both match, you get no current flow. How is this possible?

It's because of the phase changes: the current through a capacitor is 90° ahead of the voltage, and the current through the inductor is 90° behind. When the circuit is in resonance, the two cancel out. In real circuits, series resistance tends to reduce the peaks. This is called damping, and the ratio of inductive reactance to resistance is known as Q (for quality factor).

I'm not sure I like this explanation.  It is wrong about getting no current flow when the impedances match, current DOES flow - always.  But there are two things going on here, the SELF inductance and capacitance make up the characteristic impedance (Zo) of a circuit.  At  resonance the self capacitance and the self inductance do cancel each other - current always flows regardless of resonance or not, but the circuit still has a characteristic impedance which is not zero.  Basically a single circuit with an inductor and a capacitor will have a frequency (resonance) in which the current and voltage will be IN PHASE with each other, for all other frequencies the voltage and current will be OUT OF PHASE.  When you have an IN PHASE case, you get maximum real power transfer through the circuit (since power is the voltage multiplied by current, when they are in phase you get the maximum value of the multiplication). 

Characteristic impedance (Zo) is only useful when you are trying to link two circuits together.  Because both circuits may share the same resonance, but REAL power will not be transmitted to the second circuit unless they both share the same characteristic impedance. 

Lets take an example: we have a radio transmitter - circuit 1.  And we have a power supply with "transmission line" aka the wires that you want to connect to the transmitter - this is circuit 2.  Now the radio has a characteristic impedance (meaning it has a capacitance and inductance based on its makeup - all electrical bodies do, whether they are really a capacitor/inductor or just a cable, transistor, etc.)  So the radio transmitter (circuit 1) has ONE frequency in which the current and voltage will be in phase, for all other frequencies it will be out of phase.  Circuit 2 (the transmission line) also has one frequency that only allows the current/voltage inphase case.  So in order to get the power from the power supply to the radio transmitter, you want both characteristic impedances to match Zo1 = Zo2.  So lets assume we did that.  Now with radio you want to "radiate" your power into the air (we'll call the air's impedance Zo3).  This means you want to make all the space/universe around us your load.  Well it turns out that space also has a characteristic impedance, this is 377 Ohms.  So if you want to radiate as much energy into space as your power source can supply, you want to make sure that Zo1=Zo2=Zo3. 

Now lets look at a Tesla coil for the reasons in the above threads.  We again have two circuits, our primary, and our secondary.  Each circuit has its own self capacitances and inductances.  And each one leads us to the characteristic impedances (Zo1 for the primary and Zo2 for the secondary).  Well, our purpose is the exact opposite to the radio transmitter above, instead of radiating our energy into space, we want to neutralize radiation and setup the strongest oscillations that we can - to send those oscillation through the ground connection (be it a wire or the earth or whatever the bottom terminal of the secondary is connected).  Well typically in Tesla coils, the primary is made of a relatively large capacitance and a pretty low inductance at some frequency determined by those two quantities.  The secondary is an inductor of much larger inductance with a capacitance (normally the toroid, sphere at the top with respect to ground) which is very low.  So the primary is maybe microfarad capacitor and microhenry inductor and the secondary is millihenry inductor and pecofarad capacitor, so Zo1 is usually very small and Zo2 is normally VERY big - we get maximum mismatch here so no REAL power flow.  BUT, the resonant frequency of the primary matches the secondary.  So both circuits will oscillate at the same frequency and slosh the power input to them back and forth between each other, developing very large oscillations - maximum REACTIVE power, but no real power. 

By now looking at the formulas posted on the website that armagdn03 gave, you should realize that a Tesla coil can be made into a radio transmitter very easily.  Make the capacitance in the primary match the capacitance in the secondary, and make the inductors in the two equal each other as well.  This will match Zo1 and Zo2 and the resonant frequencies of both circuits will be the same.  If you match those values with that of free space (377Ohm) you'll have yourself a good little radiator.  Tesla said he invented a knife, with a dull edge and a sharp edge, you can cut butter with both sides.  Unfortunately, mankind decided it was going to use the dull edge and completely ignore the sharp one!

Quote
You said that in Tesla coils, primary and secondary need to be mismatched as much as possible. Wouldn't that imply that the energy would be wasted in the primary trying to keep the oscillations going in the secondary which is out of tune?

I think my above rant explained this but to reiterate, the energy wasted in the system is wasted on the resistance in the wires.  Those are what damps the system.  Both secondary and primary are IN TUNE with each other, they both share the same resonant frequency, with their self capacitance and inductance canceled in each individual circuit (1 and 2), but their characteristic impedances are greatly different - so the energy is just sloshed back and forth between them.

@armagdn03
What I really want to know is how you can use a "load" that just oscillates.  A vibrating tuning fork may look pretty but what is it going to do?  How can we use it, how can we convert the energy to power our resistive loads WITHOUT damping the system.  That's the real trick I want to learn here.  I'm still very intent on finding out!!!

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Re: Introduction to Resonance
« Reply #23 on: October 12, 2008, 12:51:43 AM »
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Offline amigo

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Re: Introduction to Resonance
« Reply #24 on: October 12, 2008, 02:39:59 AM »
I'm not sure I like this explanation.  It is wrong about getting no current flow when the impedances match, current DOES flow - always.  But there are two things going on here, the SELF inductance and capacitance make up the characteristic impedance (Zo) of a circuit.  At  resonance the self capacitance and the self inductance do cancel each other - current always flows regardless of resonance or not, but the circuit still has a characteristic impedance which is not zero.

Yes you are right, I think the parallel resonance graph from the page I linked is much better as a depiction than its text. The graph shows that the dip is still above the X axis so there's current flowing, just minimal amount.

Quote
Tesla said he invented a knife, with a dull edge and a sharp edge, you can cut butter with both sides.  Unfortunately, mankind decided it was going to use the dull edge and completely ignore the sharp one!

Thank you for that quote, I got a good chuckle from it. :D

Quote
I think my above rant explained this but to reiterate, the energy wasted in the system is wasted on the resistance in the wires.  Those are what damps the system.  Both secondary and primary are IN TUNE with each other, they both share the same resonant frequency, with their self capacitance and inductance canceled in each individual circuit (1 and 2), but their characteristic impedances are greatly different - so the energy is just sloshed back and forth between them.

Sorry I didn't really read the above yet, I usually go backwards and when I see large posts I tend to go back and read them in one sitting with sufficient attention and focus so that I don't miss something important.

So basically if we had a superconductor we would have no resistance and there would be no end to oscillations, otherwise we have the Q factor due to resistance?

Quote
What I really want to know is how you can use a "load" that just oscillates.  A vibrating tuning fork may look pretty but what is it going to do?  How can we use it, how can we convert the energy to power our resistive loads WITHOUT damping the system.  That's the real trick I want to learn here.  I'm still very intent on finding out!!!

I thought we'd need another transformer there in the secondary circuit to actually hook up the load. Wasn't it all going through the ground in Tesla's case so you would tap the ground to get the good stuff and would not need another transformer ? I guess the other component were Longitudinal Waves which were instantaneous (propagating at c^2 iirc from Eric Dollard's lecture).

Offline Charlie_V

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Re: Introduction to Resonance
« Reply #25 on: October 12, 2008, 03:52:13 AM »
Quote
I thought we'd need another transformer there in the secondary circuit to actually hook up the load. Wasn't it all going through the ground in Tesla's case so you would tap the ground to get the good stuff and would not need another transformer ? I guess the other component were Longitudinal Waves which were instantaneous (propagating at c^2 iirc from Eric Dollard's lecture).

I don't know about c^2 and instantaneous, I'm not that far yet.  But if you take another transformer and get it oscillating from the ground currents (which come from the secondary of the main Tesla coil - we'll call it the transmitting Tesla coil) and hook a load to this transformer, it damps the system still because you start draining the energy in the two circuits that normally would slosh back and forth.  So the power from the source that input the energy into the transmitting Tesla coil, will again have to add more energy to keep the oscillations going.  The ground oscillations allow us to use 1 wire (the ground) instead of 2 (a hot and a ground).  Basically we make the 1 wire serve as both a hot and a ground simultaneously. 

You can collect energy though from natural sources - and man made, like my coil does with 60Hz.  For example, the earth mechanically vibrates at 7.5Hertz.  Because the ground and ionosphere act as a big capacitor, when the earth vibrates it creates a weak AC wave which is normally measured to be small.  But maybe a Tesla coil tuned to this resonance could pick that up and power loads from it - who knows!

Sorry for such a long post last time.  I kinda got carried away haha - I like talking about this stuff. 

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Re: Introduction to Resonance
« Reply #25 on: October 12, 2008, 03:52:13 AM »
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Offline amigo

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Re: Introduction to Resonance
« Reply #26 on: October 12, 2008, 05:20:28 AM »
You can collect energy though from natural sources - and man made, like my coil does with 60Hz.  For example, the earth mechanically vibrates at 7.5Hertz.  Because the ground and ionosphere act as a big capacitor, when the earth vibrates it creates a weak AC wave which is normally measured to be small.  But maybe a Tesla coil tuned to this resonance could pick that up and power loads from it - who knows!

The more I look at Tesla's patents more I believe that his intention was not to use the circuits with our conventional devices. If anything, we need to create the same loads as he did in order to tap into it and get useful work out. And you know that he had built lots of custom light bulbs, motors and such items that ran on his circuits no problem.

I think we are just trying to push a square peg through a round hole and it won't work, but we still keep trying never the less. I keep saying about it all the time but it falls on def ears. Moment there's a possibility about some alternative device producing energy, people try to short circuit it so it runs on conventional loads. It's like trying to bring the mountain to yourself, when it's much much easier to just take the trip to the mountain and be blessed with beautiful sights, clean air, rocks and trees and flowing streams of water.

Quote
Sorry for such a long post last time.  I kinda got carried away haha - I like talking about this stuff.

Hey, you and me both, but that's great because it gets the ideas going, information is exchanged, and we are both richer at the end. :D

Offline Charlie_V

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Re: Introduction to Resonance
« Reply #27 on: October 12, 2008, 06:06:48 AM »
Yea, I think you are right, he did make custom loads.  In his day these loads still had a chance since electricity was new.  There was a possibility of everyone going down his route but unfortunately they didn't. 

I'm interested in finding ways to power the devices we have today.  It would be hard to come up with different types and actually market them, you'd almost have to start over - 200 years invested on the types of loads we have now.  They built a mountain of trash, it would be really difficult to try to topple it.  Instead I want to recycle that trash by finding a clever way of using the loads we have, I know its possible because the universe itself MUST function with both energy consuming and regenerating - this must be balanced.  Whatever energy is going downhill in the universe there is a mechanism that is bringing it back up the hill, no one has figured out what that is - but I know it is there, otherwise we would not exist. 

I have some ideas I'm trying but right now its slow going.  Its only a matter of time before someone figures it out.  I think armagdn03 is right when he says there are ways to use the same energy over and over again.  The trick is going to be a way to link the regenerative part to the resistive part without damping.  There are a million ways to skin a cat, we just need to find the cat first hahaha! 

I'm off to bed, good night.

Offline amigo

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Re: Introduction to Resonance
« Reply #28 on: October 12, 2008, 06:29:24 AM »
You have a capacitor of 0.2 micro farads and a resistor of 20,000 ohms.  Lets assume we use a 10,000V source that can supply 1amps.  We have a spark gap so that when the capacitor reaches 10kV the spark gap discharges into a 4 micro henry inductor of very low resistance (i.e. large wires).  So, the capacitor and inductor make a tank circuit when the spark gap discharges.

The time it requires to charge the capacitor up to 10,000V is roughly 0.004 seconds.  Since the capacitor is discharged so rapidly when the gap fires, we can neglect the fall time of the capacitor.  This means that we can fire the gap at about 250 times in one second (250Hz).  How much energy is in the capacitor when it dumps into the inductor? 
E=0.5*C*V^2
So the there are 10 Joules in the capacitor when it fires.  We are inputting P=10/0.004, about 2500 Watts of power into the tank circuit.  HOWEVER! What is the power in the tank circuit - it is NOT 2500 Watts!  The resonant circuit oscillates at 177,940 Hz [ f = 1/(2*PI*sqrt(LC)) ].  The time constant of the tank circuit is 5.6 micro seconds!!!  The energy in the capacitor is still 10 Joules, so the power of the oscillation is 10/5.6micro which is equal to about 1.779 Mega Watts (1,779,406 Watts). 

Do we have over unity?  No we don't, that is because that 1.8 mega watts of power is all reactive.  This means that the 10 Joules of energy is only tossed back and forth between the capacitor and inductor 177,940 times in one second but the amount of energy in the system does not change (just 10 Watts and decreasing due to resistance).

Could you please elaborate on the numbers here since I am kinda confused. I see where you got the 0.004 sec for charging (ref: http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/capchg.html#c2) but I am puzzled about your power computation and the pure reactive power. This is where I'm looking for reference http://www.sayedsaad.com/fundmental/66_OHMS%20LAW%20FOR%20AC%20.htm which is basically NEETS in colour.

According to that page, reactive power is based on reactive current and total reactance, but we are in resonance so wouldn't that make X=0 |XL-XC| making the whole circuit only resistive with true power of 5KW, or did I get all this wrong?

Offline Charlie_V

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Re: Introduction to Resonance
« Reply #29 on: October 12, 2008, 05:11:49 PM »
The time it takes a capacitor to charge up is R*C (resistance times capacitance).  The energy the capacitor stores is E = 0.5*C*V^2 (one half times the capacitance times the voltage squared).  With a voltage of 10,000 Volts, and a capacitance of 0.2microfarads, the energy in the capacitor is 10Joules.  Power is Joules divided by seconds.  Since the capacitor discharges into an inductor of neglectable resistance, the time constant for discharging is basically zero and the only wait time we have is the charging time constant (which was 0.004 seconds).  Therefore, with our spark gap set to fire when the capacitor reaches 10kV, the power we are inputting to the capacitor (which dumps into the inductor) is 10/0.004 or 2500Watts.

When the spark gap fires, it shorts the power supply and essentially disconnects the capacitor, leaving the capacitor and inductor as a separate circuit for a certain amount of time until the spark in the gap goes out.  In this instant of time, the capacitor and inductor form a tank circuit with no load.  The capacitor (disconnected by the closed spark gap from the power supply) dumps its energy into the inductor.  The inductor, in-turn, takes that energy and dumps it back into the capacitor.  The energy continues to slosh back and forth between the two components at a frequency of f = 1/(2*PI*sqrt(LC)) = 177,940 Hz.  If you read about tank circuit resonance, you will find that the energy sloshing in the tank circuit is purely reactive.  In one instant, the capacitor is charged and no current flows in the inductor.  In the next instant all the current is flowing and there is no voltage in the capacitor.  Basically, the current and voltage in an oscillating tank circuit are 90 degrees out of phase, this is purely reactive power.  The resistance of the tank circuit damps it, otherwise it would ring like that forever - so I suppose in a real situation there is a small amount real power being consumed due to wire resistance, if we used super conductors it will oscillate indefinitely.

In fact, by putting a load on the tank circuit, it won't oscillate at all.  The capacitor will dump that 2500 Watts into the load once, if it is a light bulb it will light up one time.  However, if you start charging and discharging the capacitor at  177,940Hz you will be putting the most energy into the load that can be placed.  If you go higher or lower than 177,940Hz, the light bulb will not be as bright.  In the case of a loaded tank circuit, the tank turns into a filter and it guarantees that only signals input at its resonant frequency will fully reach the load.

Quote
According to that page, reactive power is based on reactive current and total reactance, but we are in resonance so wouldn't that make X=0 |XL-XC| making the whole circuit only resistive with true power of 5KW, or did I get all this wrong?

That's because that website is talking about apples and not oranges.  It is explaining how a circuit acts if you are trying to input energy to a load that has a "filter" within it.  Yes, if you have a load with some reactance and you want to give it the most power, you want your input frequency (your power supply frequency) to match the resonant frequency of that "filter".  If you take away the load from the filter, and are left with just the filter, at resonance the energy will just slosh back and forth and you'll only get reactive power.  Basically the energy you send to the filter will bounce back if there is no load to absorb the energy.  You will rarely find a website that talks about energy bounce back simplistically because it is something they try to avoid (and is rarely thought about and understood - I think).  Radio websites give the best details into this matter. 
http://www.ycars.org/EFRA/Module%20C/TLSWR.htm
Read the linked page of this website (but just this first page that I have linked - making sure to watch the "click here" videos - because other sections of this guys website are crappy).  This one page gives a really good simple explanation of how energy can bounce back in an electrical system.

Hope that helps!

 

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