How capacitor blocks dc current?

[Ratch]

Pythagorean,

You can describe the surface of the Earth in spatial coordinates much like you describe the state of the elements of a circuit in "I-V space". Pick any coordinate system, xyz or phi/theta/r. All eigenbases are still orthogonal.

Cartesian to polar coordinate transform is only valid in orthogonal systems. It applies to circuits as well as space

A state is the minimum set of variables needed to describe your system. For instance, a particle has position and velocity in it's state vector, [x,p]. A complex number is a single number, but can also represent two numbers if you think of it as a vector instead. In fact, j (or i) is just an orthogonal transform operator.

How is this going to help anyone do circuit analysis, especially figuring out whether a capacitor blocks DC current?

Ratch

 

[Pythagorean]

Pythagorean,How is this going to help anyone do circuit analysis, especially figuring out whether a capacitor blocks DC current?

Ratch

I'm not sure why you suddenly bring up pedagogy. My posting is in response to this:

Reactance of a coil or capacitor is a complex quantity, and it needs its "j".

Perhaps this is the pedagogical benefit, though; that if you use vectors instead of complex values, you won't get confused into thinking real measurable values are complex. This is probably only relevant to a science/math student though. If you're purpose is only electrical engineering, it's unlikely you'll see complex numbers in any other context, so it's probably never an issue.

 

[Ratch]

Pythagorean,

I'm not sure why you suddenly bring up pedagogy. My posting is in response to this:


Reactance of a coil or capacitor is a complex quantity, and it needs its "j".

I did not think an Earth coordinate system had any relevance to circuit analysis.

Perhaps this is the pedagogical benefit, though; that if you use vectors instead of complex values, you won't get confused into thinking real measurable values are complex. This is probably only relevant to a science/math student though. If you're purpose is only electrical engineering, it's unlikely you'll see complex numbers in any other context, so it's probably never an issue.

I believe the energy stored in the electric field of a capacitor or the magnetic field of an inductor is every bit as "real" as the energy dissipated in a resistor. Yet that reactive energy is designated as "complex" in a sinusoidal circuit.

Ratch

 

[SunnyBoyNY]

Perhaps this is the pedagogical benefit, though; that if you use vectors instead of complex values, you won't get confused into thinking real measurable values are complex.

To my understanding the two approaches are (and ought to be) equivalent in the end.

In the big picture we could:

1) Use the usual circuit model, set up differential equations, do a nightmarish trigonometry (or transform to vectors and then do complex algebra to get the result.
2) Immediately switch to the impedance-based circuit model and do complex algebra to get the final result.

Bts. measurable values can be and are complex with respect one to another. E.g. power factor measurement. In that case we of course need multiple measurements.

This is probably only relevant to a science/math student though. If you're purpose is only electrical engineering, it's unlikely you'll see complex numbers in any other context, so it's probably never an issue.

Complex numbers are used throughout the EE field. Non-linear systems analysis, adaptive filtering, etc. While your vector-based example is interesting, it has little in common with the actual problem.

 

[Studiot]

this also means that reactance is negative for capacitors and positive for inductors (e.g. -500 Ohms for a capacitor as suggested by sophiecentaur).

As long as '"j" gets tacked on at some point, I am happy.

Reactance of a coil or capacitor is a complex quantity

You seem to have some difficulty with terminology.

We distinguish three distinct types of numbers (there are others but they are irrelevant in this context)

Real numbers,
imaginary numbers which can be expressed as the product of a real number and j
complex numbers which canbe expressed as the sum of a real number and and an imaginary number.

Each have their own special properties.

In particular only real numbers can be positive or negative.
So one of the above quotes is false.

A reactance is a real number, usually given the sign X.

This may be combined with j into an imaginary number and added to or subtracted from a real resistance to achieve a complex impedance.

Impedance, admittance and reactance are not inherently complex quantities.

I can show you a good book that says that immittance is not a phasor quantity, but is a complex quantity. It has to be. What else can you get when you divide a sinusoidal voltage by a sinusoidal current?

You get exactly what I wrote in post #90 a real modulus and a real phase angle.

They can be specified using a real modulus and a real phase angle and the calculations performed by trigonometry. Not is single i, j or k will be seen.

Exponential representation can be easily converted into rectangular or polar form by Euler's Theorem. Anytime the angle θ is not zero, there is a reactance involved, and an implied orthogonal component to the term.

So what?
I can convert or transform 3 into 6 by doubling.
Again so what?

Of course all valid methods must produce the same answer from the same data.

Your posts seem to imply that there only method available is that of complex analysis, which is simply not the case.

 

[Ratch]

Studiot,

You seem to have some difficulty with terminology.

How so?

imaginary numbers which can be expressed as the product of a real number and j

Due to its conformal similarity, multiplying by "j" gives correct answers. But "j" is really a rotational operator, not a algebraic term. For instance, 4j does not mean j+j+j+j. It really means rotate 4 by 90° CCW. The term "imaginary" has been applied to them, but they are every bit as real as the numbers along the reference line. They instead should be called something like "orthogonal numbers".

In particular only real numbers can be positive or negative. So one of the above quotes is false.

Not so. For instance, -4j means rotate (-4) 90° CCW or -4j = -j4 means rotate (4) 90° CW.

A reactance is a real number, usually given the sign X.

As long as it gets rotated in the right direction, everything will be OK.

This may be combined with j into an imaginary number and added to or subtracted from a real resistance to achieve a complex impedance.

Certainly.

Impedance, admittance and reactance are not inherently complex quantities.

I can show you a good book that says that immittance is not a phasor quantity, but is a complex quantity. It has to be. What else can you get when you divide a sinusoidal voltage by a sinusoidal current?


You get exactly what I wrote in post #90 a real modulus and a real phase angle.

Things equal to the same thing are equal to each other.

So what?
I can convert or transform 3 into 6 by doubling.
Again so what?

You have to ask that question to whom I was replying.

Your posts seem to imply that there only method available is that of complex analysis, which is simply not the case.

I never said anything about uniqueness or exclusivity.

Ratch

 

[Pythagorean]

To my understanding the two approaches are (and ought to be) equivalent in the end.

In the big picture we could:

1) Use the usual circuit model, set up differential equations, do a nightmarish trigonometry (or transform to vectors and then do complex algebra to get the result.
2) Immediately switch to the impedance-based circuit model and do complex algebra to get the final result.

Bts. measurable values can be and are complex with respect one to another. E.g. power factor measurement. In that case we of course need multiple measurements.
Complex numbers are used throughout the EE field. Non-linear systems analysis, adaptive filtering, etc. While your vector-based example is interesting, it has little in common with the actual problem.

That they are equivalent is the point.

i.e., the point is that they are not intrinsically complex, they are a only convenient way of orthogonal vector handling. For instance in quantum mechanics, the Hilbert Space is actually a complex space and observables are actually complex operators. When you compute the expectation value, it resolves to a real number.

 

[Pythagorean]

Pythagorean,



I did not think an Earth coordinate system had any relevance to circuit analysis.



I believe the energy stored in the electric field of a capacitor or the magnetic field of an inductor is every bit as "real" as the energy dissipated in a resistor. Yet that reactive energy is designated as "complex" in a sinusoidal circuit.

Ratch

It's not actually complex though (no more than in spatial coordinates that Earth is in). The maths of complex numbers is just exploited here for convenience, that's the point. Quantum mechanics, on the other hand, really uses a complex Hilbert Space and complex operators for observables.

 

[Ratch]

Pythagorean,

It's not actually complex though (no more than in spatial coordinates that Earth is in). The maths of complex numbers is just exploited here for convenience, that's the point. Quantum mechanics, on the other hand, really uses a complex Hilbert Space and complex operators for observables.

Whatever.

Ratch

 

[Studiot]

So is (3+2.5j) positive or negative?

 

[Ratch]

Studiot,

So is (3+2.5j) positive or negative?

A duplex number like that has no positive or negative direction. You can only determine the positivity or negativity of its real and orthogonal components.

Ratch

 

[Studiot]

Exactly.

And what of the current complexor?

Oh and duplex means bidirectional

 

[Ratch]

Studiot,

Exactly.

Exactly what?

And what of the current complexor?

The current complex order? Please elucidate.

Oh and duplex means bidirectional

It also means twofold or double, as in a duplex apartment, as in the number you asked about.

Ratch

 

[webberfolds]

https://www.physicsforums.com/showthread.php?t=6065. Read the 5th post. I don't know why people say the current passes, it's weird!

hello

Capacitors are widely used in electronic circuits to block the flow of direct current while allowing alternating current to pass,how it does the job?

samieee

 

[psparky]

My definition of "J" is quite simple in my view.

J= 1<90 degrees. A vector with a magnitude of 1 pointing straight up at 90 degrees.

We all know that J*J=-1. That's because 1<90 degrees X 1<90 degrees = 1<180 degrees...also known as -1.

When I see this number: (3+2.5j)
I actually see 3<0 +(2.5*1<90) or simply 3<0 + 2.5<90.

If you think of J in these terms, I think it simplyfies things quite a bit.

 

[sophiecentaur]

I think you need to be careful about simply saying that "j = 90degrees".
It happens that you can draw a vector version (phasor) of a time varying sinusoid and that the j operator can be represented by an angle in this limited geometrical way. It's the same with Argand diagrams. But 'j' exists outside of geometry and the forms that it's commonly represented by.

 

[psparky]

I think you need to be careful about simply saying that "j = 90degrees".
It happens that you can draw a vector version (phasor) of a time varying sinusoid and that the j operator can be represented by an angle in this limited geometrical way. It's the same with Argand diagrams. But 'j' exists outside of geometry and the forms that it's commonly represented by.

I agree for some of the "super brains" of this forum. But for normal people, especially people trying to grasp "J"...my definition should take them a long way.

If you are implying that reference point of voltage isn't always zero...then sure, the "J" will be 90degrees off the reference point.

To this point in time, I have never been asked a question where my definition wouldn't satisfy the answer. But I certainly agree with your point.

By the way...who is this "Argand" fellow?

 

[psparky]

And to the point of this thread, I've never been a big physics guy when it comes to electricity...(explaining the charged plates and all that).

But I just follow the math.
Current flows thru a cap according to this C*(dv/(dt))=i(t)
In other words...no change in voltage...no current flow. (this supports caps blocking DC)
It's impedance also supports this : 0(R) + 1/(jwc) When w=0, impedance becomes infinite (caps block DC)
Actually, it's 0(R) + J*(-1/wc) Same thing...proper form for impedance I suppose.

In opposite similar fashion, L*di/dt=vt and Jwl define the "shorts" of an inductor in DC.

The 1/jwc and jwl will not be true in transients...only steady state. The other two definitions should always hold true.

 

[sophiecentaur]

I came across Mr. Argand long before phasors and calculus. Look him up. He's responsible for the Complex Plane and solutions of algebraic equations etc.. wiki rules.