# Parallel resonance concerning RL and Rc

## Main Question or Discussion Point

Hello,
my question this time is once again about parallel resonance. I cant really decipher this paragraph from my text:

'....the resistances of a parallel circuit are of signal importance in determining the frequency of resonance, even to the extent of making resonance either possible or impossible to attain. Physically this can be understood when it is remembered that, with a certain quadrature component of current in the capacitive branch, some sufficiently large value of RL will prevent a resultant current in the inductive branch from flowing, which is as much as the quadrature current in the capacitive branch even when the inductance is zero.
Under such condition it is apparent that inserting inductance will do nothing but make the current in the inductive branch still smaller and hence contribute nothing toward making resonance possible.....'

Okay, according to the bolded parts, how come the currents blocked by RL even when the inductance is zero?
And second, isn't the current minimal during parallel resonance anyways? So what does that (second bolded) line mean then?

Thank you

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jim hardy
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Try this, it Might help i dont know...

electrical resonance is important and its exactly the same equations you see in harmonic motoin in physics class.

Okay, according to the bolded parts, how come the currents blocked by RL even when the inductance is zero?
Wow that sounds like a hard way to teach it.

draw yourself a picture... and observe
1. It's PARALLEL connection of an L in one leg and a C in other leg.
2. The L is not ideal so there's series resistance in that leg.
3. When that resistance becomes larger than X, the current in inductive leg must be smaller than the current in capacitive leg. That's because they're in PARALLEL so have the same voltage across them and I = V/Z. Even if one of the Z's has become all R and no X.

And second, isn't the current minimal during parallel resonance anyways?
Aha - Which current is minimal? Let's make R zero for a moment...
The externally supplied current at resonance becomes very small but the individual currents through capacitor leg and inductor leg are still V/X which can be quite large.

Since current in capacitor leg LEADS by 90° and current in inductor leg LAGS by 90°,
they're 180° out of phase and ideally have sum of zero. That's what must be externally supplied, their sum (remember good ol' Kirchoff), and it's doggone small but the leg currents are large.

Now start increasing R of inductor and the current in L leg is no longer at 90° lag so the sum of currents is no longer so small. They no longer cancel.
As that resistance approaches X , lagging current through R-L leg comes more closely in phase with applied voltage. So it no longer cancels the other leg and the current dawn from source goes up.

Now parse this phrase carefully:
0R... L will prevent a resultant current in the inductive branch from flowing, which is as much as the quadrature current in the capacitive branch even when the inductance is zero.
It's just ohm's law.
current is Volts / Ohms in both legs.
In one leg ohms is -jXc and in other it's R+jXl.. What happens when R=mag(jXc) ? Even if jXl is 0 ?

So what does that (second bolded) line mean then?
If there's resonance the capacitor and inductor are swapping energy back and forth at resonant frequency.
When resistance of inductor leg gets large enough it absorbs as much energy as was stored in inductor every cycle. Capacitor no longer knows there's an inductor out there so it swaps energy back and forth with source instead. There's no more L-C resonance.

Please excuse my colloquialisms. I find that quote from your text very awkward and not a logical development of thought. It needed some lightening up.

Do you still draw phasor diagrams of current and solve these things with rectangular and polar notation? Did they give you homework problems?
Have they shown you "Q" yet?

"Q" is ratio of energy stored to energy dissipated per cycle so is obviously related to R and X. Basically it's X/R. It also defines 'damping' , rate of decay. Q below .707 is overdamped and doesn't oscillate .

Your leg currents will be V/Z and your external current will be ~ (leg current)/Q

hang in there. the concept is easy and it will come as you work the problems. Do lots of them.

Most of us learn in sequence What then Why. That quote from your text is an attempt at "Why", did it mention "What" earlier?

We all learn learn by doing so work the exercises. I hope they're practical with real numbers.

Last edited:
Try this, it Might help i dont know...

electrical resonance is important and its exactly the same equations you see in harmonic motoin in physics class.

Wow that sounds like a hard way to teach it.

draw yourself a picture... and observe
1. It's PARALLEL connection of an L in one leg and a C in other leg.
2. The L is not ideal so there's series resistance in that leg.
3. When that resistance becomes larger than X, the current in inductive leg must be smaller than the current in capacitive leg. That's because they're in PARALLEL so have the same voltage across them and I = V/Z. Even if one of the Z's has become all R and no X.

Aha - Which current is minimal? Let's make R zero for a moment...
The externally supplied current at resonance becomes very small but the individual currents through capacitor leg and inductor leg are still V/X which can be quite large.

Since current in capacitor leg LEADS by 90° and current in inductor leg LAGS by 90°,
they're 180° out of phase and ideally have sum of zero. That's what must be externally supplied, their sum (remember good ol' Kirchoff), and it's doggone small but the leg currents are large.

Now start increasing R of inductor and the current in L leg is no longer at 90° lag so the sum of currents is no longer so small. They no longer cancel.
As that resistance approaches X , lagging current through R-L leg comes more closely in phase with applied voltage. So it no longer cancels the other leg and the current dawn from source goes up.

Now parse this phrase carefully:
It's just ohm's law.
current is Volts / Ohms in both legs.
In one leg ohms is -jXc and in other it's R+jXl.. What happens when R=mag(jXc) ? Even if jXl is 0 ?

If there's resonance the capacitor and inductor are swapping energy back and forth at resonant frequency.
When resistance of inductor leg gets large enough it absorbs as much energy as was stored in inductor every cycle. Capacitor no longer knows there's an inductor out there so it swaps energy back and forth with source instead. There's no more L-C resonance.

Please excuse my colloquialisms. I find that quote from your text very awkward and not a logical development of thought. It needed some lightening up.

Do you still draw phasor diagrams of current and solve these things with rectangular and polar notation? Did they give you homework problems?
Have they shown you "Q" yet?

"Q" is ratio of energy stored to energy dissipated per cycle so is obviously related to R and X. Basically it's X/R. It also defines 'damping' , rate of decay. Q below .707 is overdamped and doesn't oscillate .

Your leg currents will be V/Z and your external current will be ~ (leg current)/Q

hang in there. the concept is easy and it will come as you work the problems. Do lots of them.

Most of us learn in sequence What then Why. That quote from your text is an attempt at "Why", did it mention "What" earlier?

We all learn learn by doing so work the exercises. I hope they're practical with real numbers.

Thanks ALOT, that got alot of confusions cleared from my head :)

And as for what asked, yes we do these stuffs with phasor diagrams, (circle diagrams) and rectangular/polar notations. We are done with Q too (except that I didn't revise it yet). Our lecturer did not give us any particular problems to solve, she just told us to work them out from our text exercises and also, this part of the concept wasn't stressed for our quiz but I couldn't get over it without knowing how it really works. About the 'what' and 'why'...lol the 'what' part is there and i guess i managed that somehow but, most of the book is difficult to comprehend; so I wanted to ask... which book would you really suggest that would nicely somewhat convey all these details?
Thank you once again.

jim hardy
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which book would you really suggest that would nicely somewhat convey all these details?
Let me think on that.
I learned resonance in 1962 high school electronics class. Our teacher was a very practical engineer who'd been a radioman in the merchant marine and i do not remember what if any text we used. He was a master explainer.

I am thinking your text is not a practical one so you need something to counterbalance it.
ARRL Radio Amateur Handbook is an excellent source.
In general the older the book the more practical.

I'll poke around the internet and look for a good site.
Years ago Bill Beatty and Don Lancaster both wrote a lot for the hobbyist genre and they are both good explainers. Peruse Bill's Amasci.com and its links, likewise Don's tinaja.com.

I will see if i still have some old textbooks. I;ll wager Yungman knows of some. Also - look into "nuts and volts" magazine, a very practical-oriented publication.

EDIT PS thanks for the kind words - i was worried you'd be insulted by my lowbrow thinkiing.

sophiecentaur
Gold Member
Okay, according to the bolded parts, how come the currents blocked by RL even when the inductance is zero?
And second, isn't the current minimal during parallel resonance anyways? So what does that (second bolded) line mean then?

Thank you
If the parallel inductance is zero then there will be no (Parallel) resonance. Any component in parallel with the C will have a finite L (even just the connecting wire of an out-of-the-drawer resistor. Take this element away and the circuit becomes a CR network of some kind.

The statement that the current is a minimum at resonance is referring to the current flowing into the parallel circuit from the signal source. There will be very high currents flowing around the LC loop, at the peaks of the cycle which will cause a high voltage across it - opposing the flow of current from the source.

Adding resistances in an LC resonator can reduce the Q factor, of course, so that the resonance is as broad and undefined as you care to make it. But isn't that 'obvious'?

jim hardy
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But isn't that 'obvious'?
We tend to forget what it was like before we knew. As did the fellow who wrote that paragraph in OP's textbook. His economy of words invites an anemic understanding, IMHO.

That's the trouble with "publish or perish" , textbooks get targeted at professorial peers instead of students. IMHO at least.

For basics I search out textbooks from 1930 to 1960.

sophiecentaur
Gold Member
For basics I search out textbooks from 1930 to 1960.
Me too but 'these youngsters' need coloured photographs and short chapters for their input. Unfortunately though, there tends to be a real shortage of 'book work' to show how they actually get the formulae in modern books. I just love those endless pages of small typeface and B/W diagrams. You really feel you're getting something from the horse's mouth.

(Note to self: don't be so sodding grumpy!)

jim hardy
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2019 Award
Dearly Missed
'these youngsters' need coloured photographs and short chapters for their input.
i knew a teacher years ago said "Wait till the Sesame Street generation hits college. They'll have no attention span. "
I thought she was being facetious.
But I can't condemn Sesame Street. It was too well done.
Instead i say "We are Madison Avenued to death. " Meaning life today has become a series of thirty second diversions.

I just love those endless pages of small typeface and B/W diagrams.
The diagrams to go with the derivations is effective for picture thinkers like me. My main references were my physics book (Sears and Zemansky) and Mark's ME handbook. And of course Thompson's "Dynamo Electric Machinery" (1901 edition).
One can get most formulas he needs for an industial maintenance job from first principles.

I picked up Moby Dick the other day. Am going to re-read it because i can't find my Bozorth Ferromagnetism.
"Just say NO" to thirty second distractions.

sophiecentaur
Gold Member
It really is worrying because these guys will still need to be able to maintain concentration for my five hour surgical operation or my next emergency manual plane landing under adverse conditions.

My Zemanski, Heat and Thermodynamics is still up there on a shelf. (Danged hard, I seem to remember)

Should we ask for a separate Forum called "Memory Lane"?

jim hardy