mutual capacitance?

Mutual capacitance does exist, e.g. the capacitance between the plates of a differential (3-plate) variable capacitor. Actually, mutual capacitance is the usual kind of capacitance we think about. There's also self-capacitance, e.g. the self capacitance of a 1-cm diameter sphere in free space is 1.12 pF. (The cgs unit of capacitance is the centimetre.)

Cheers

Phil Hobbs

Because the physically relevant quantity of a circuit is the complex impedance. There is a mutual complex impedance, that includes the effects of all linear electronic elements. The complex impedance is analogous to the resistance, but it includes all linear circuit quantities: the resistance, the capacitances and the inductances. The complex impedance of an inductor is sqrt(-1)(angular frequency) (inductance). The complex impedance of a capacitor is 1/ sqrt(-1)(angular frequency)(capacitance). The complex impedance of a resistor is the real part of the complex impedance. The complex impedance of a circuit is analogous to the resistance. There is a total complex impedance of a circuit is calculated using the well known equations for total resistance taught in elementary school, only with complex number. The total resistance of the circuit is simply the real part of the total complex impedance calculated this way. One can define a mutual inductance and a mutual capacitance from the imaginary part of the mutual complex impedance. However, the mutual inductance will be determined by the mutual capacitance, and vica versa. All properties important to the circuit as a whole are contained in the mutual complex impedance. The analogy that your subconscious is working on is likely to be the complex impedance. This is more important in problems involving AC current than for DC current. However, current passing through a circuit with capacitors and inductors can't be DC (i.e., steady) anyway. The complex impedance of a circuit can be calculated by formulas analogous to the formulas for total resistance in DC current. So I recommend that you look up complex impedance. I think a lot of things will come clear when you understand the concept.

Mutual? I thought that your question was about _dual_ elements.

A dual relation arises when current and voltage are exchanged.

For a capacitor the relation between current and voltage is:

I = C * dV/dt

Exchanging I and V, we must include inductance:

V = L * dI/dt

Hence, a capacitor is dual to an inductor.

Yes. But also for the usual frequencies real capacitors are closer to ideal than real inductors. For coupling between nearby transmission lines, such as multiple twisted pairs in one cable, both inductance and capacitance are important.

-- glen

(snip)

Yes. What is dual to a transformer? (Coupled inductors)

-- glen

so, essentially, every plate has mutual capacitance with every other plate, throw a term in for the angle between them and sum, or what ever.

That's a very strange statement to make. How would you define "ideal"? Surely an ideal inductor has zero resistance and zero diameter wire with as many turns as you like, wound on a bobbin of no length and no diameter, all turns of the same length, and that's before considering the core material. The ideal capacitor has plates with any area you choose and a zero gap between them, yet do not touch, and that's before considering the dialectric material between them. Neither can be ideal.

For coupling between nearby | transmission lines, such as multiple twisted pairs in one cable, | both inductance and capacitance are important. | | > Actually, mutual | > capacitance is the usual kind of capacitance we think about. There's | > also self-capacitance, e.g. the self capacitance of a 1-cm diameter | > sphere in free space is 1.12 pF. (The cgs unit of capacitance is the | > centimetre.) | | -- glen |

The other day I wanted to determine the corner frequency of an RC circuit that feeds into an opamp. I couldn't 'break' into the circuit to inject a little test signal, so I wrapped a bit of plastic coated wire about the lead going into the opamp. This formed a bit of ? mutual? capacitance between the wire and lead. (Each has separate capacitance to ground.) I then sent a square wave into the wire, and this gave me little charge pulses into the opamp/ RC circuit.

I'm not sure if this maps mathematically into mutual inductance,

George H.

what network theorem is that ?

obviously you are wrong. Magnetic fields lines are closed loops, no magnetic monopoles, and E fields bi-polar.

(snip)

Sounds more like mutual capacitance.

Some years ago I was working on measuring the capacitance of test devices (they were electrochemical solar cells, but that doesn't really matter.)

Similar to your example, you put some AC voltage across the capacitor and measure the current. Interestingly, the lead bringing the voltage in, and the one measuring the current, can each have much higher capacitance to ground than the capacitor being measured. (Use a lock-in amplifier to detect the result, measuring the voltage across a resistor.)

Another way to measure the capacitance is to put a small current through it and measure the voltage, inversely proportional to C.

-- glen

(snip on duality)

Reminds me of an undergrad physics lecture demonstration showing the equivalence between open and closed end air columns (organ pipes), and open and shorted coaxial transmission lines.

During the demonstration, the lecturer figured out that the analogy was backwards. The closed tube (pressure antinode) coresponds to the open end coax (voltage antinode).

To correct this, the next lecture had the same setup, but with a current probe on the oscilloscope. Shorted end is a current antinode.

Some might have tried to explain away the difference, and not bother with the current probe. Now I still remember it over thirty years later.

-- glen

A good reference is Smythe's Static and Dynamic Electricity.

Almost all capacitance we deal with is mutual capacitance. Two conductors are involved, For a conductor a and a conductor b, the self capacitance is the charge divided potential difference produced on one conductor as if none of the other conductors were present. Essentially, it is the capacitance to infinity. That is, self capacitances Caa = Qa/Vainfinity and Cbb = Qb/Vbinfinity. Using cgs electric units, the self capacitance of a sphere is its radius in centimeters.

Mutual capacitance Vab = Qab/Vab. It is the charge change produced on a and b divided by the change of potential difference used to produce the charge.

A network theorem states that every circuit has a dual; voltage sources become current sources, etc.

But, what about mutual inductance? Why is there no mutual capacitance? By symmetry, shouldn't a 'mutual capacitor' exist, linking electric flux?

-- Rich

------------------------ Mutual capacitance does exist. One practical case is a multiconductor power transmission lines where there is capacitance coupling between conductors and to images of conductors. One can form a Potential coefficient matrix P which based on V=PQ. The form of the terms in this matrix are analogous to the inductance matrix and involve terms of the form ln Dij/Hij where D is the distance between conductors i, j and H is the distance from conductor i to the image of j The inverse of P is a capacitance matrix where the Cii terms are "self" capacitances and the Cij terms are the "mutual" capacitances. In the inductor case one looks at self and mutual impedances and in the capacitor case, the dual is self and mutual admittances.

Don Kelly cross out to reply

(snip)

Yes. What is dual to a transformer? (Coupled inductors)

-- glen

------------------------------------ v1=L11(di1/dt) +L12 (di2/dt) V2=L21(di1/dt) +L22(di2/dt)

inductive coupling

vs

I1 =C11(dv1/dt) +C12(dv2/dt) I2=C21(dv1/dt) +C22(dv2/dt)

Capacitive coupling

It exists-grab a fence wire parallel to and under a transmission line- get the benefit of C21(dv1/dt) where I2 is the current through your body- a real world problem.

Don Kelly cross out to reply

Depends what you mean by "exist". While as others have pointed out there is mutual capacitance, it isn't really a true dual to a transformer. The true dual is the capacitive transformer which retains all the features of a magnetic transformer. Generally speaking the device doesn't exist except in certain special circumstances, but it's widely used as a theoretical aid to network calculations. Like gyrators and some other oddball network elements they do not widely exist as physical passive elements, but there are certain cases (certain piezo devices) where they almost exist. They can be made to exist using active simulation. And who needs a device if you have the equations? Today, we all believe mathematics is more real than reality anyway!

"Phil Hobbs" napisal w wiadomosci news: snipped-for-privacy@electrooptical.net...

Itis for 2-cm diameter. But how much pF has 4-cm diameter sphere? S*

It is not backwards. Pressure and voltage are the same.

Shorted ends are like a loop dipole.

So is time to understand it. Electron gas is like air. The one arm of a dipole is like Kund's tube. S*

"Salmon Egg" napisa³ w wiadomo¶ci news: snipped-for-privacy@news60.forteinc.com...

Benj wrote: "Today, we all believe mathematics is more real than reality anyway!"

In reality the "self capacitance of a sphere " is its surface and radius dependent. S*

Capacitance is proportional to the radius. If not, the unit would not be cm. To figure it out, find the capacitance between concentric spheres in the limit that the outer sphere radius goes to infinity.

For an extra check, find the capacitance of two concentric spheres of constant spacing (delta r) as the radii increases. For r >> dr, it is proportional to r squared, as you would expect.

-- glen