## How capacitor blocks dc current?

SunnyboyNY,

 Could we reach some sort of compromise?
Perhaps, on some things.

 1) No DC or AC current physically flows through a capacitor. The current seen at the terminals of such part is simply a charge being removed or added to the plates. The net charge on the plates is constant.
I agree with the above. I will even say that current exists in the branch where the cap is located, even if the current does not pass through the cap.

 2) The complex impedance equation has been established to quantify frequency-dependent current magnitude and phase on the device terminals with respect to other circuit elements.
I would say that the complex impedance term has been established to describe the orthoganality between the voltage and current responses of energy storage elements (caps and coils) and energy dissipative elements (resistors).

 3) Perhaps we could all agree that a capacitor can certainly be energized, when the voltage across the dielectric insulator is non-zero. Whether the term is charged or energized is left to the discretion of debater.
After all, energized means "charged with energy", right?

 4) As of the original question, capacitors block DC current in steady state. Steady-state is characterized as a time interval where all energy-storage elements carry the same energy in the beginning as in the end. In other words, once the transient state is finished, average capacitor voltage is constant. Since capacitor energy is dependent on its voltage, the total charge stored on the plates is constant at the two time intervals. Thus, DC component of current flowing through the capacitor ought to be zero.
If you are only referring to DC, then energy levels need not be considered to define steady state. I would say that steady state occurs when time is relatively long and no change occurs in the cap voltage. I would change your statement to say the the current in the capacitor branch becomes zero. The current through the cap was always zero

 5) In reality, the steady-state is determined by the lowest-frequency eigenvalue in the system. Say the capacitor is charged and discharged in one second intervals; the period is two seconds. Capacitor voltage stays the same, which suggests zero DC component of the current. Non-steady state situation such as initial charge simply have infinite period.
I am going to stick with a long period of time as defining steady state. We can define the cap's DC component by its average voltage value. By capacitor voltage staying the same, I hope you mean the voltage at the beginning and end of the period as being zero. Since the voltage is a positive pulse for a 2 second period, there will be a positive DC component. I don't understand what you mean by initial voltage having a infinite period.

Ratch
 Recognitions: Gold Member Science Advisor Umm. I'm not sure what current flowing "physically" means. Let's ignore the electrons bit because that just clouds the issue. A current flows in one end and out of the other end of a resistor or a capacitor. Kirchoff's laws work perfectly well in most circuits. How are the two cases different? Is it really worth labouring the point that 'charging a capacitor' is not the same thing as 'charging' a comb by rubbing it? Capacitors and batteries are what we discuss in circuit theory - not isolated / insulated objects. I think we agree that 'yer actual DC' does not exist, because that would involve infinite time for it to be established. So, if DC is a pragmatic term for 'constant value for long enough', then the reactance (let's just call it Impedance, in fact) to DC is just as meaningful as at any frequency of AC. At our newly defined version of DC frequency (<0.0001Hz, say), the impedance is (to all intents and purposes) infinite. But I still don't see why you guys don't want to use Maths (or at least refer to it) to describe what goes on. The exponential charge / discharge of a CR network describes exactly what goes on and that can be re-stated in terms of frequencies and Impedance. The results of experiment agree so well with that simple theory and it isn't difficult to approach the 'ideal case' in practice. That's why we can design filters and other circuits to work in such a predictable way. Discussing "what's really happening" is not really getting one any closer to an understanding unless you really want to get into QM and how materials behave.

sophiecentaur,

 Umm. I'm not sure what current flowing "physically" means.
You will never observe me using the phrase "current flow". That literally means "charge flow flow", which is redundant and ridiculous. Charge does not flow twice, so you are correct to wonder about it. I always refer to current as "existing" or "passing through" or having a "direction", but never flowing. Charge can flow, however.

 Let's ignore the electrons bit because that just clouds the issue.
Electrons cannot be ignored. They are the primary charge carriers in metals. When electrons move, current exists.

 A current flows in one end and out of the other end of a resistor or a capacitor. Kirchoff's laws work perfectly well in most circuits. How are the two cases different?
Kirchoff's Current Law (KCL) is not violated in either case. Here's why. KCL simply says that all charges have to be conserved. They cannot travel down a wire and just disappear. There is no problem with charges passing through a resistor, but it is a little more subtle when charges encounter a capacitor. A capacitor is a energy storage element, and it stores charges on one side of the dielectric insulator and supplies electrons from the opposite of the dielectric, as I said several times before. This separation and accumulation of electrons causes a back voltage to form which diminishes the current in the branch containing the capacitor. It takes energy to accumulate and deplete the electrons, and this energy is stored in an electric field within the dielectric. Nevertheless, every electron is accounted for according to KCL. There is also a transitory current in the circuit branch containing the capacitor.

 Is it really worth labouring the point that 'charging a capacitor' is not the same thing as 'charging' a comb by rubbing it?
It is good to know how a capacitor works, even if it is different than generating high voltage by rubbing a comb.

 I think we agree that 'yer actual DC' does not exist, because that would involve infinite time for it to be established. So, if DC is a pragmatic term for 'constant value for long enough', then the reactance (let's just call it Impedance, in fact) to DC is just as meaningful as at any frequency of AC. At our newly defined version of DC frequency (<0.0001Hz, say), the impedance is (to all intents and purposes) infinite.
A capacitor is going to follow its energizing voltage. Unless there is no resistance in the circuit, it will have a time delay that a resistor does not have. This time delay is caused by having to imbalance or even out the charge between its plates. A capacitor energized by a step voltage of constant amplitude will have an impedance whose magnitude is infinite, but with an orthoginal orientation. That makes it different than just an open circuit. Mathematically, it is described as -j∞.

 But I still don't see why you guys don't want to use Maths (or at least refer to it) to describe what goes on. The exponential charge / discharge of a CR network describes exactly what goes on and that can be re-stated in terms of frequencies and Impedance. The results of experiment agree so well with that simple theory and it isn't difficult to approach the 'ideal case' in practice. That's why we can design filters and other circuits to work in such a predictable way.
We are using a minimum of mathematics, because for nonsinusoidal circuits, differential equations (DE) are necessary to calculate and understand the response. Not everyone is up to speed on DE.

 Discussing "what's really happening" is not really getting one any closer to an understanding unless you really want to get into QM and how materials behave.
I think we are closer to the micro level than the quantum level. I do think it is necessary to understand what really goes on rather than using hydraulic analogies and other fool's aids to describe what is not really happening.

Ratch

Recognitions:
Gold Member
 Quote by Ratch I do think it is necessary to understand what really goes on rather than using hydraulic analogies and other fool's aids to describe what is not really happening. Ratch
I am pleased that we are at one in that respect!
 A capacitor is going to follow its energizing voltage. Unless there is no resistance in the circuit, it will have a time delay that a resistor does not have. This time delay is caused by having to imbalance or even out the charge between its plates. A capacitor energized by a step voltage of constant amplitude will have an impedance whose magnitude is infinite, but with an orthoginal orientation. That makes it different than just an open circuit. Mathematically, it is described as -j∞.
Not sure what this all means. It is a bit wooly and you appear to be wanting to make a distinction that is quite artificial. You are mixing your domains here, in any case. 'Impedance' and 'orthogonal' are frequency domain terms and 'step function' is a time domain term.

sophiecentaur,

 'Impedance' and 'orthogonal' are frequency domain terms
They shouldn't be. You can't plot a frequency spectrum from a impedance, and orthogonal is simply a definition which means "at right angle to".

Ratch

Recognitions:
Gold Member
 Quote by Ratch sophiecentaur, They shouldn't be. You can't plot a frequency spectrum from a impedance, and orthogonal is simply a definition which means "at right angle to". Ratch
Time and frequency domains are interchangeable with the appropriate transforms but the appropriate operations in each domain are different. Impedance refers to the ratio of Volts to Current for a given frequency. It's a 'frequency domain term'. It is used to calculate the effect of a circuit component on the frequency spectrum of a signal. Can you show an example where Impedance comes into the description of an operation in the time domain (without some sort of transform being involved)? If you want to work in the time domain then you need to specify impulse responses and not impedances.

Is there a "right angles' (I think you actually mean 90 degree phase, in this context) in the time domain? In fact, of course, the term Orthogonal has many other connotations than just "at right angles".

I guess this flurry of attempted pedantry is due to a perceived slight concerning "current flow". In fact, if you read back, you'll see that I was picking up on someone else's post and not yours so you can calm down.

sophiecentaur,

 Impedance refers to the ratio of Volts to Current for a given frequency. It's a 'frequency domain term'.
All right, I will concede that impedance is frequency dependent if storage elements are involved.

 Is there a "right angles' (I think you actually mean 90 degree phase, in this context) in the time domain? In fact, of course, the term Orthogonal has many other connotations than just "at right angles".
Yes, I was. As in a duplex (complex) number, where x + jy means x units on a reference scale and b units on a scale 90° CCW from it.

 I guess this flurry of attempted pedantry is due to a perceived slight concerning "current flow". In fact, if you read back, you'll see that I was picking up on someone else's post and not yours so you can calm down.
You guessed wrong on that one. I was not even thinking of "current flow" when I answered your post.

Ratch

Recognitions:
Gold Member
 Quote by Ratch sophiecentaur, All right, I will concede that impedance is frequency dependent if storage elements are involved. Yes, I was. As in a duplex (complex) number, where x + jy means x units on a reference scale and b units on a scale 90° CCW from it. You guessed wrong on that one. I was not even thinking of "current flow" when I answered your post. Ratch
I don't understand that at all. Surely you can describe the reactance of a pure resistor as beingzero just the same as the reactance of a 'capacitor' can be -753Ω. You seem to have a problem with 'zeros' in this business - as, also, with DC means f=0. What's so special about "storage elements"?

sophiecentaur,

 I don't understand that at all.
What don't you understand?

 Surely you can describe the reactance of a pure resistor as being zero just the same as the reactance of a 'capacitor' can be -753Ω.
Certainly the reactance of an ideal resistor is zero ohms, and it also has a real part that is frequency independent. The reactance of the ideal capacitor you to which you refer would be -j753 ohms, and have no real frequency independent component.

 You seem to have a problem with 'zeros' in this business - as, also, with DC means f=0.
That seems to be a simple enough concept. What make to think that?

 What's so special about "storage elements"?
Their ability to receive energy from the circuit, and return the same energy back to the circuit at a different times, makes their voltage and currents different than nonstorage elements like resistors which dissipate energy away from the circuit. This is best observed in sinusoidal waveforms where phase differences occur between current and voltage of coils and caps, but no phase differences are present in resistive components.

Ratch
 Recognitions: Gold Member Science Advisor The term "storage element" is a bit too non-specific, to my mind. After all, you can make a simple chemical battery with virtually no reactive impedance (certainly no inherent reactance). Why not just use the term 'Reactive'? And, incidentally (I expected you to pick me up on this one so I looked in wiki and other places, to make sure I got it right) X stands for reactance and is measured in Ohms. Impedance is a complex quantity and is R+jX. So the reactance of a Capacitor is -1/ωC, with no j. I was correct to quote a reactance of -753Ω. If it were not this way, we would write Z = R + X Pedantry can turn round and bite you. I suggested that you may have a problem with zeros because, on two occasions, you have treated a zero value (Reactance or Frequency) as somehow different from finite values.

sophiecentaur,

 The term "storage element" is a bit too non-specific, to my mind. After all, you can make a simple chemical battery with virtually no reactive impedance (certainly no inherent reactance).
The term "storage element" does indeed describe a coil and capacitor, but it is not a comprehensive definition. A battery or DC supply acts differently because they do not take energy from the circuit and return it later. "Reactive" also describes coils and capacitors, but does not describe the storage aspects of those elements. The bottom line is that one cannot describe everything about an object in one word.

 the reactance of a Capacitor is -1/ωC, with no j. I was correct to quote a reactance of -753Ω.
Wiki is wrong abou that, as they are wrong about a lot of things. Reactance of a coil or capacitor is a complex quantity, and it needs its "j". Look at the link below, and notice that they get it right. If you don't put in a "j", then how do you distinguish a reactance from a resistance mathematically?

 Pedantry can turn round and bite you.
Not this time.

 I suggested that you may have a problem with zeros because, on two occasions, you have treated a zero value (Reactance or Frequency) as somehow different from finite values.
Infinities and infinitesimals have to be treated with caution. Perhaps you can provide an example in a previous post where I have been wrong about that subject. I hate to be wrong.

Ratch

http://www.st-andrews.ac.uk/~www_pa/...lex/react.html

 Quote by Ratch The term "storage element" does indeed describe a coil and capacitor, but it is not a comprehensive definition. A battery or DC supply acts differently because they do not take energy from the circuit and return it later. "Reactive" also describes coils and capacitors, but does not describe the storage aspects of those elements. The bottom line is that one cannot describe everything about an object in one word.
The term storage element is circuit analysis is bound to inductive and capacitive elements, because those are the ones causing dynamic behavior. Reactive impedance are equal to the eigenvalues of a system (poles).

A battery could be simply modeled as a huge capacitor such that the associated eigenvalue would be so small that all other pertinent transients would be long finished before the battery energy changes ever-so-slightly. Since poles in typical RLC circuits are rather fast, we could reduce the order of the system by modeling a battery by a constant voltage source.

SunnyBoyNY,

 A battery could be simply modeled as a huge capacitor....
A huge capacitor will resonate with a huge coil; a battery will not. As I mentioned before, a battery does not take energy from the circuit and return it back in equal amounts at a different time as a capacitor would. Therefore, resonance is not possible with a battery, and the circuit will not respond the same way to huge capacitor as it would to a battery.

Ratch

 Quote by Ratch SunnyBoyNY, A huge capacitor will resonate with a huge coil; a battery will not. As I mentioned before, a battery does not take energy from the circuit and return it back in equal amounts at a different time as a capacitor would. Therefore, resonance is not possible with a battery, and the circuit will not respond the same way to huge capacitor as it would to a battery. Ratch
A non-ideal battery will not resonate with a coil because a good-battery model consists of a number of non-linear elements. A large capacitor is one of them. In an LC circuit energy flow reverses when one element is completely discharged and the other is fully charged. That impossible to do with a battery that is almost completely depleted at a voltage not far from its maximum.

The approximation of a battery as a large capacitor would be valid for analysis where the run time is much shorter than the resonant frequency of the battery model and the smallest galvanically connected inductance coil in the circuit.

How else would you model a charge-dependent voltage source? Say ones wants to model a battery powering a dc/dc converter that has an LC output filter and a resistive load. The battery voltage (=capacitor voltage with an initial condition) will drop over time because there is no other initial energy in the system. The converter will go through a number of cycles that will not be affected by the additional capacitive element at all.

SunnyboyNY,

 A non-ideal battery will not resonate with a coil because a good-battery model consists of a number of non-linear elements.[ How else would you model a charge-dependent voltage source? Say ones wants to model a battery powering a dc/dc converter that has an LC output filter and a resistive load. .....
This thread is concerned with linear circuits, not nonlinear ones. That means linear elements. Also, you are drifting off topic by asking for nonlinear models that work conditionally for specific situations.

For the reasons I gave before, a battery is not a universal linear substitute for a capacitor.

Ratch

 Quote by Ratch For the reasons I gave before, a battery is not a universal linear substitute for a capacitor. Ratch
If we are limited to linear circuits then a battery is simply modeled as a voltage source combined with small-value series resistor and inductor. Provided low-importance of such parasitic components we can reduce the model to a simple voltage source.

Recognitions:
Gold Member
 Quote by Ratch sophiecentaur, The term "storage element" does indeed describe a coil and capacitor, but it is not a comprehensive definition. A battery or DC supply acts differently because they do not take energy from the circuit and return it later. "Reactive" also describes coils and capacitors, but does not describe the storage aspects of those elements. The bottom line is that one cannot describe everything about an object in one word. Wiki is wrong about that, as they are wrong about a lot of things. Reactance of a coil or capacitor is a complex quantity, and it needs its "j". Look at the link below, and notice that they get it right. If you don't put in a "j", then how do you distinguish a reactance from a resistance mathematically? Not this time. Infinities and infinitesimals have to be treated with caution. Perhaps you can provide an example in a previous post where I have been wrong about that subject. I hate to be wrong. Ratch http://www.st-andrews.ac.uk/~www_pa/...lex/react.html
The battery in my car does just that and so does the one in my iPod. You can't assign it an equivalent capacity either because it doesn't have an exponential time characteristic when discharging or charging through a resistor.

It's not just wiki. It is everywhere. X stands for reactance. The Impedance of a reactance X is jX. Check it out.

I agree in principle but I don't think that there is much of a problem in the 'limits' in these cases, though.