How Does Increasing Frequency Affect Capacitor Voltage in an RC Circuit?

[k31453]

Lets say if i got RC series circuit.

If i increase the voltage supply frequency then what happen to the voltage across a capacitor ??

I rekon the voltage going to increases and the I going to decrease to negligible.

 

[psparky]

Due to it's impedance of 1/jωc, increasing frequency (ω) will lower the impedance of the capacitor. As you raise the frequency, the resistor (R) will start to gain voltage and the capacitor (c) will start to drop in voltage.

As far as negible voltage across the capacitor, this will be true if your frequency is super high. If the frequency is moderate, the capacitor may have a decent amount of voltage across it. It's just a math equation, or simple voltage division in this case.

 

[k31453]

Thanks

 

[anhnha]

Hi,
Do the formulas Zc = 1/jωc and ZL = jωL apply for other voltage shape like square, sawtooth waves?

 

[Runei]

The formulas you show are the impedance's of a capacitor and an inductor. These formulas are always correct, and they can be used with square and sawtooth waves.

HOWEVER, in order to use them, you will have to decompose the square wave or sawtooth wave (or any signal shape) into it's constituent components, and to do this, you need to know Fourier Analysis.

Do you have any experience with Fourier or Laplace transforms?

 

[anhnha]

The formulas you show are the impedance's of a capacitor and an inductor. These formulas are always correct, and they can be used with square and sawtooth waves.

HOWEVER, in order to use them, you will have to decompose the square wave or sawtooth wave (or any signal shape) into it's constituent components, and to do this, you need to know Fourier Analysis.

Do you have any experience with Fourier or Laplace transforms?

Thanks Runei,
I know these transforms. And therefore, there are different frequencies and different impedance for each frequency.
Ah, it seems to me that it is like a filter, right?

 

[Runei]

You are completely right. And actually, it IS a filter :)

 

[psparky]

Don't forget about your C*dv/dt=it and L*di/dt=vt

They also always hold true. (ideal conditions of course)

 

[Windadct]

To help keep the logic straight - DC is F=0 - at this point capacitors are at 0 current, and inductors are pure conductors. This boundary condition is alwas a good test of your logic - since the f=0 - is easily dropped into the math as well.

 

[anhnha]

Hi,
I got a bit confused, hope anyone can help!
For example, I have a AC voltage source with various frequencies from very low frequency (DC) to ultra-high frequencies (UHF). The voltage source is connected in parallel with an ideal capacitor. At very high frequencies, the capacitor will be short because Zc = 1/ωC is very small, almost zero.
Will this short damage the voltage source?

 

[sherrellbc]

Hi,
I got a bit confused, hope anyone can help!
For example, I have a AC voltage source with various frequencies from very low frequency (DC) to ultra-high frequencies (UHF). The voltage source is connected in parallel with an ideal capacitor. At very high frequencies, the capacitor will be short because Zc = 1/ωC is very small, almost zero.
Will this short damage the voltage source?

As far as I know a short circuit is a short circuit regardless of situation. That being said, the supply would definitely be shorted - although the damage would be a function of its protective circuitry.

 

[technician]

To be precise you should refer to the 'reactance' of a capacitor and an inductor.
Reactance is given as X_c = 1/ωC for a capacitor and X_L = ωL
Impedance is the combination of resistance and reactance.
For R and C in series the impedance is given by Z² = R² + X_C²
I don't think you will find Z_C used to represent the reactance of a capacitor
You will not find Z² = R² + Z_C² in a textbook

Check the hyperphysics site for more detail

 

[anhnha]

As far as I know a short circuit is a short circuit regardless of situation. That being said, the supply would definitely be shorted - although the damage would be a function of its protective circuitry.

Hi,
For example, in this circuit there are two capacitors that are used to filter out low and high frequencies.

I don't see protective circuitry anywhere. At very high frenquencies, the ceramic capacitor will be source and will this damage the bridge rectifier?

To be precise you should refer to the 'reactance' of a capacitor and an inductor.
Reactance is given as X_c = 1/ωC for a capacitor and X_L = ωL
Impedance is the combination of resistance and reactance.
For R and C in series the impedance is given by Z² = R² + X_C²
I don't think you will find Z_C used to represent the reactance of a capacitor
You will not find Z² = R² + Z_C² in a textbook

Check the hyperphysics site for more detail

I know these formulas but my assumption that the capacitor is ideal!

 

[technician]

If the capacitor is ideal, with zero resistance, then you have only capacitative reactance X_C

 

[meBigGuy]

Hi,
Do the formulas Zc = 1/jωc and ZL = jωL apply for other voltage shape like square, sawtooth waves?

The formulas you show are the impedance's of a capacitor and an inductor. These formulas are always correct, and they can be used with square and sawtooth waves.

HOWEVER, in order to use them, you will have to decompose the square wave or sawtooth wave (or any signal shape) into it's constituent components, and to do this, you need to know Fourier Analysis.

Do you have any experience with Fourier or Laplace transforms?

I'd like to state this in a more accurate way.

The formulas only apply to sine waves. In order to use them with complex waveforms you must de-compose the complex waveform into its sine waves (all infinitely repeating waveforms can be decomposed into sine waves).

The responders seem to be making this much more confusing that it really is.

It is technically incorrect to say a capacitor across an AC supply will "short" the supply. It will provide a complex load determined by its reactance and resistance and the supply will respond accordingly.

The voltage across a series LC circuit becomes 0 at the series resonant frequency (for ideal components) even though the reactance of the L and C are non-zero at that frequency. In fact, at resonance they have equal reactance and opposite phase, which cancels. If you configure and analyze a divider using the formulas you wrote above, you can solve for the voltage across the capacitor.

 

[milesyoung]

I don't see protective circuitry anywhere. At very high frenquencies, the ceramic capacitor will be source and will this damage the bridge rectifier?

For ideal components, your circuit (without the diode bridge) would draw extremely large currents if you impressed a voltage on the transformer primary with a frequency in the upper RF bands. That won't happen, though, for components that are physically realizable. Foremost, the frequency response of the grid transformer will have low-pass characteristics and you'll generally have parasitic inductance just about everywhere. Maybe you've seen these types of charts before for the impedance of real capacitors as a function of frequency:

http://www.analog.com/library/analogdialogue/archives/39-09/3909_01.gif

You'll notice that they start to behave an awful lot like inductors when you pass their resonance frequency.

Edit:
I wanted to give you an idea of what would happen if you had a situation as per your post #10. If you include the diode bridge without actually loading the rectifier (assuming ideal components) it will just draw an extremely large inrush current until the smoothing capacitance is charged.

To be precise you should refer to the 'reactance' of a capacitor and an inductor.

There's nothing wrong or imprecise about referring to the impedance of an ideal capacitor and/or an inductor. There's a very significant difference between impedance and reactance, but it has to do with complex numbers.

I have a friend who's a very good electrician. He talks about impedance and reactance in the same fashion you do since he was taught a version of AC analysis where only the magnitude of the impedance mattered, because that was mainly what was needed in sizing components and such. In this way, he didn't need to learn the theory of complex numbers, which really wouldn't benefit him a great deal in his work anyway.

That version of AC analysis is not the whole story and it's not what you're taught as an electrical engineer. I can't rule out every university/college of course, but I highly doubt any would define impedance as you do.

 

[technician]

For ideal components, your circuit (without the diode bridge) would draw extremely large currents if you impressed a voltage on the transformer primary with a frequency in the upper RF bands. That won't happen, though, for components that are physically realizable. Foremost, the frequency response of the grid transformer will have low-pass characteristics and you'll generally have parasitic inductance just about everywhere. Maybe you've seen these types of charts before for the impedance of real capacitors as a function of frequency:

http://www.analog.com/library/analogdialogue/archives/39-09/3909_01.gif

You'll notice that they start to behave an awful lot like inductors when you pass their resonance frequency.

Edit:
I wanted to give you an idea of what would happen if you had a situation as per your post #10. If you include the diode bridge without actually loading the rectifier (assuming ideal components) it will just draw an extremely large inrush current until the smoothing capacitance is charged.


There's nothing wrong or imprecise about referring to the impedance of an ideal capacitor and/or an inductor. There's a very significant difference between impedance and reactance, but it has to do with complex numbers.

I have a friend who's a very good electrician. He talks about impedance and reactance in the same fashion you do since he was taught a version of AC analysis where only the magnitude of the impedance mattered, because that was mainly what was needed in sizing components and such. In this way, he didn't need to learn the theory of complex numbers, which really wouldn't benefit him a great deal in his work anyway.

That version of AC analysis is not the whole story and it's not what you're taught as an electrical engineer. I can't rule out every university/college of course, but I highly doubt any would define impedance as you do.

There is a difference between reactance and impedance and it has nothing to do with complex numbers!
Complex numbers is a branch of mathematics that is very useful in many areas of physics. Complex numbers are not AC theory.
Reactance and impedance are 2 different terms that have different meanings and their difference does not require a knowledge of complex numbers. ( if anything all you need to recognise is Pythagoras theorem).
You should check some basic school and college textbooks (and the hyperphysics site) to gain greater insight into the meaning of these terms.
The difficulty is on a par with referring to a weight of 1kg...I am sure this would be corrected here.

Do you have access to suitable textbooks?

 

[milesyoung]

There is a difference between reactance and impedance and it has nothing to do with complex numbers!

Then I doubt you have studied electrical engineering.

You should check some basic school and college textbooks (and the hyperphysics site) to gain greater insight into the meaning of these terms.

Here's two textbooks I often see recommended for freshman/sophomore EE courses:

Electric Circuits, 9th Edition, Nilsson, Riedel, ISBN-13: 978-0-13-611499-4.
Excerpt from p. 320 under the heading "Impedance and Reactance":

Solving for Z in Eq. 9.35, you can see that impedance is the ratio of a circuit element's voltage phasor to its current phasor. Thus the impedance of a resistor is R, the impedance of an inductor is jωL, the impedance of mutual inductance is jωM, and the impedance of a capacitor is 1/(jωC). In all cases, impedance is measured in ohms. Note that, although impedance is a complex number, it is not a phasor. Remember, a phasor is a complex number that shows up as the coefficient of e^(jωt). Thus, although all phasors are complex numbers, not all complex numbers are phasors.

Engineering Circuit Analysis, 7th Edition, Hayt, Kemmerly, Durbin, ISBN-13: 978-0-07-286611-7.
Excerpt from p. 387 under the heading "Impedance":

Let us define the ratio of the phasor voltage to the phasor current as the impedance, symbolized by the letter Z. The impedance is a complex quantity having the dimensions of ohms.

Here's a textbook I used in my first year for my bachelor's degree in EE/mechatronics:

Basic Engineering Circuit Analysis, 9th Edition, Irwin, Nelms, ISBN-13: 978-0470-23455-6.
Excerpt from p. 389 under the heading "Impedance and Admittance":

Impedance is defined as the ratio of the phasor voltage V to the phasor current I at the two terminals of the element related to one another by the passive sign convention, as illustrated in Fig. 8.9. Since V and I are complex, the impedance Z is complex and since Z is the ratio of V to I, the units of Z are ohms.

I don't claim that these are great, or even good, books. I do claim that they present the basics correctly.

And with regards to the HyperPhysics site:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imped.html

You'll notice, under the heading "Impedance":

More general is the complex impedance method.

which is what you're taught in EE courses. You should also notice the abundance of complex numbers throughout the rest of that page.

Maybe it's best if we just agree to disagree so we don't derail yet another thread.

 

[technician]

Then I doubt you have studied electrical engineering.Here's two textbooks I often see recommended for freshman/sophomore EE courses:

Electric Circuits, 9th Edition, Nilsson, Riedel, ISBN-13: 978-0-13-611499-4.
Excerpt from p. 320 under the heading "Impedance and Reactance":Engineering Circuit Analysis, 7th Edition, Hayt, Kemmerly, Durbin, ISBN-13: 978-0-07-286611-7.
Excerpt from p. 387 under the heading "Impedance"ere's a textbook I used in my first year for my bachelor degree in EE/mechatronics:

Basic Engineering Circuit Analysis, 9th Edition, Irwin, Nelms, ISBN-13: 978-0470-23455-6.
Except from p. 389 under the heading "Impedance and Admittance":I don't claim that these are great, or even good, books. I do claim that they present the basics correctly.

And with regards to the HyperPhysics site:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imped.html

You'll notice, under the heading "Impedance":which is what you're taught in EE courses. You should also notice the abundance of complex numbers throughout the rest of that page.

Maybe it's best if we just agree to disagree so we don't derail yet another thread.

OK.
I have studied electrical engineering and fully realize the value of complex numbers.
I had no problem grasping AC theory before complex numbers were introduced. They are a mathematical tool...that is all

Ps...the definition impedance = V/I I totally agree with

 

[milesyoung]

I had no problem grasping AC theory before complex numbers were introduced. They are a mathematical tool...that is all.

That's good, but I didn't write what I did to discuss complex numbers. I wrote it because you're using a definition of impedance that discards the phase information that's included with the use of complex numbers and that is one which I highly doubt is part of any college/university EE curriculum.

Ps...the definition impedance = V/I I totally agree with

But you realize that V and I are phasors, i.e. they're not real numbers, as in they're not in ℝ? Thus impedance Z cannot, in general, be a real number. The magnitude of Z, which is what you find with |Z| = √(R² + X²), is a real number.

Edit:
This PF library entry goes into greater detail:
https://www.physicsforums.com/library.php?do=view_item&itemid=303

 

[jim hardy]

To a question asked partway down the thread (#13)

Hi,
For example, in this circuit there are two capacitors that are used to filter out low and high frequencies.

I don't see protective circuitry anywhere. At very high frenquencies, the ceramic capacitor will be source and will this damage the bridge rectifier?



I know these formulas but my assumption that the capacitor is ideal!

The 78xx is protected internally against DC overcurrent.

Very high frequency on incoming power lines will be attenuated by the inductance of a non-ideal (ie a real) transformer, protecting downstream parts from a source to the left..

The ceramic capacitors are there to keep the 78xx stable at high frequency. The regulator is a gain element with feedback so is capable of oscillation. Low dropout types are particularly susceptible. The ceramic capacitor keeps the regulator itself from becoming a high frequency source.


http://cds.linear.com/docs/en/application-note/an83f.pdf
http://www.analog.com/library/analogdialogue/archives/45-01/bypass_capacitors.html
http://www.ti.com/lit/an/snva167a/snva167a.pdf
http://www.ti.com/lit/an/snva167a/snva167a.pdf

 

[technician]

That's good, but I didn't write what I did to discuss complex numbers. I wrote it because you're using a definition of impedance that discards the phase information that's included with the use of complex numbers and that is one which I highly doubt is part of any college/university EE curriculum.But you realize that V and I are phasors, i.e. they're not real numbers, as in they're not in ℝ? Thus impedance Z cannot, in general, be a real number. The magnitude of Z, which is what you find with |Z| = R² + X², is a real number.

Edit:
This PF library entry goes into greater detail:
https://www.physicsforums.com/library.php?do=view_item&itemid=303

I am perfectly happy to stick with Z² = R² + X²
Where Z means impedance, R means resistance and X means reactance (magnitudes thereof)

 

[milesyoung]

I am perfectly happy to stick with Z² = R² + X²
Where Z means impedance, R means resistance and X means reactance (magnitudes thereof)

Right, so you'd agree that the impedance of an ideal capacitor and inductor is given by 1/(jωC) and jωL, respectively?

 

[technician]

Right, so you'd agree that the impedance of an ideal capacitor and inductor is given by 1/(jωC) and jωL, respectively?

Only when analysis of AC circuits is by means of complex numbers.
In the case of analysis without complex numbers (this is completely possible) it seems that we agree that reactance of a capacitor is 1/ωC and reactance of an inductor is ωL and resistance is R.
ie. V_C/I_C = X_C

And didn't we agree to not go off subject?
I am OK with what we have now.

 

[milesyoung]

Only when analysis of AC circuits is by means of complex numbers.

But that's entirely the point. Your idea of impedance is not the one shared by EE students (who define impedance as a complex quantity), which is why when you write things like:

To be precise you should refer to the 'reactance' of a capacitor and an inductor.

You are, in my opinion, doing them a disservice by asserting something which really isn't true.

Now, I think I have been more than reasonable with regards to your requests:

You should check some basic school and college textbooks (and the hyperphysics site) to gain greater insight into the meaning of these terms.

What did you expect me to find? Where are those college textbooks that define impedance in other terms than what I have shown?

 

[technician]

But that's entirely the point. Your idea of impedance is not the one shared by EE students (who define impedance as a complex quantity), which is why when you write things like:

First of all it is not 'my idea' If you have never met complex numbers there is no alternative.
The hyperphysics site shows X_C = 1/ωC and X_L = ωL and then states that the contribution to complex impedance is -j/ωC and jωL

A simple search for reactance (Wiki etc) is exactly what I would say.
I hesitate to say it but... I am a teacher...(ready to accept insults) and I teach students who study physics but do not do maths and do not know what complex numbers are. It is not their fault, it is not my fault...they love physics and they have no problems with understanding AC theory. If I was to tell them they could not do AC theory until they had met complex numbers THEN I would be doing them a disservice.

This is definately my final comment in this thread.

 

[milesyoung]

I would certainly not ask you to stop teaching AC theory to your students, in fact, I commend you for it. I'm saying that, if it's clear that someone is using the definition of impedance as a complex number, which is perfectly reasonable in the context of EE, we should work within that framework.

 

[technician]

I would certainly not ask you to stop teaching AC theory to your students, in fact, I commend you for it. I'm saying that, if it's clear that someone is using the definition of impedance as a complex number, which is perfectly reasonable in the context of EE, we should work within that framework.

OK... I am with you, this is an EE thread so I suppose the assumption must be that the original
post has some idea about complex analysis. It is hard to tell what the level of the OP is, I err on the side that they are beginners and maths may not be a strong point.
This is a good thread, I appreciate your comments and they have not degenerated into a slagging match !
Which can so easily happen here.

 

[jim hardy]

I hesitate to say it but... I am a teacher...(ready to accept insults) and I teach students who study physics but do not do maths and do not know what complex numbers are. It is not their fault, it is not my fault...they love physics and they have no problems with understanding AC theory. If I was to tell them they could not do AC theory until they had met complex numbers THEN I would be doing them a disservice.

I don't know what level your students are
and doubtless things have changed since the 1960's.

We were taught complex numbers and phasors in a high school electronics class, starting in tenth grade. 8th grade Geometry and Trig and 9th grade Algebra are all one needed . We boys had no difficulty, in fact got quite skilled at rectangular to polar conversions with slide rules and AC circuit analysis became second nature...

Teaching high school kids to do the mechanics of complex arithmetic necessary for AC circuit analysis I should think will enrich their experience..

 

[meBigGuy]

There is a difference between reactance and impedance and it has nothing to do with complex numbers!
Complex numbers is a branch of mathematics that is very useful in many areas of physics. Complex numbers are not AC theory.
Reactance and impedance are 2 different terms that have different meanings and their difference does not require a knowledge of complex numbers. ( if anything all you need to recognise is Pythagoras theorem).
You should check some basic school and college textbooks (and the hyperphysics site) to gain greater insight into the meaning of these terms.
The difficulty is on a par with referring to a weight of 1kg...I am sure this would be corrected here.

Do you have access to suitable textbooks?

You are hopelessly out of your depth now. You are totally wrong. Reactance is the complex portion of the impedance. Period. End of Issue. What do you think the j is in the formulas given above? it is square root of -1, an "imaginary" number. AC theory is ALL about frequency and phase, which is another way of representing complex numbers. The magnitude and the phase represent the hypotenuse of a triangle in the complex plane (actually, a vector in the complex plane) , and the real and imaginary parts are the opposite and adjacent.

You can use high school shortcuts like the ones you mention, but they show a complete lack of understanding of the math behind AC analysis.

Read the wikipedia entry on Impedance and then use the above complex formulas for reactance to properly derive the series resonant frequency where the inductive and capacitive reactance are equal and opposite. Then, use them to derive voltage vs. frequency across the capacitor in a series resonant circuit. Then come back and drop the attitude.

 

[technician]

I agree completely with you Jim...I am also a 'child of the 60s'.I fully recognise the application and value of complex numbers in physics. But I would still emphasise that they are a mathematical tool, they are not essential and at the level I teach (A level +) a full understanding of the behaviour of AC circuits can be obtained with straight forward geometrical vector diagrams ...the next step to using complex notation is easy but there is not time to go into that in the physics course.
I very much appreciate your comments, not just in this thread but in your excellent posts regarding electronics...I recognise your 60s background in what you write !

 

[meBigGuy]

I recognize your lack of background in what you write. Please read the wikipedia entry on Impedance.

 

[meBigGuy]

a full understanding of the behaviour of AC circuits can be obtained with straight forward geometrical vector diagrams

Yes, that is how one does analysis of complex quantities.

 

[jim hardy]

... a full understanding of the behaviour of AC circuits can be obtained with straight forward geometrical vector diagrams ...the next step to using complex notation is easy but there is not time to go into that in the physics course...

Indeed in only a one or two semester general physics course I see why you don't go into it.

My high school had a 2 hour per day three year almost vo-tech electronics course, but with more math than prior vocational curricula. Our school board was reacting to Sputnik and tried out a few pre-engineering high school courses. So we had plenty of time to learn and drill complex arithmetic. I must say I likely would not have made it through EE school without the practical background from that electronics course. Familiarity with rotating phasor notaion made 3 phase seem natural.

Thanks for the kind words...

Your practical teachings will doubtless influence some kids.

old jim