mutual capacitance?

[RichD]

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

 

[Phil Hobbs]

RichD wrote:

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, 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

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics Electro-optics Photonics Analog Electronics

55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058

email: hobbs (atsign) electrooptical (period) net
http://electrooptical.net

 

[Chris Richardson]

On Fri, 17 Jun 2011 10:49:17 -0700, RichD wrote:

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

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.

 

[Androcles]

"glen herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in message
news:itga64$9o4$1@dont-email.me...
| In sci.physics.electromag Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:
| > RichD wrote:
| >> 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?
|
| > Mutual capacitance does exist, e.g. the capacitance between the plates
| > of a differential (3-plate) variable capacitor.
|
| Yes. But also for the usual frequencies real capacitors are closer
| to ideal than real inductors.

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
|

 

[huhie]

"RichD" <r_delaney2001@yahoo.com> wrote in message
news:f8b96838-84f7-4e19-b352-f470595ebeb8@k15g2000pri.googlegroups.com...

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

what network theorem is that ?

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

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

--
Rich

 

[Darwin123]

On Jun 17, 1:49 pm, RichD <r_delaney2...@yahoo.com> wrote:

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

 

[glen herrmannsfeldt]

In sci.physics.electromag Phil Hobbs <pcdhSpamMeSenseless@electrooptical.net> wrote:

RichD wrote:
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?

Mutual capacitance does exist, e.g. the capacitance between the plates
of a differential (3-plate) variable capacitor.

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.

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

 

[glen herrmannsfeldt]

In sci.physics.electromag Chris Richardson <root@localhost.localdomain> wrote:

(snip)

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

-- glen

 

[1treePetrifiedForestLane]

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.

 

[George Herold]

On Jun 17, 1:49 pm, RichD <r_delaney2...@yahoo.com> wrote:

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

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.

 

[glen herrmannsfeldt]

(sci.math removed)
In sci.physics.electromag George Herold <gherold@teachspin.com> wrote:

(snip)

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,

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

 

[glen herrmannsfeldt]

In sci.physics.electromag huhie <invalid@invalid.invalid> wrote:

(snip on duality)

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

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

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

 

[Salmon Egg]

In article
<f8b96838-84f7-4e19-b352-f470595ebeb8@k15g2000pri.googlegroups.com>,
RichD <r_delaney2001@yahoo.com> wrote:

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

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.

--

Sam

Conservatives are against Darwinism but for natural selection.
Liberals are for Darwinism but totally against any selection.

 

[Don Kelly]

"RichD" wrote in message
news:f8b96838-84f7-4e19-b352-f470595ebeb8@k15g2000pri.googlegroups.com...

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

 

[Don Kelly]

"glen herrmannsfeldt" wrote in message news:itga9f$9o4$2@dont-email.me...

In sci.physics.electromag Chris Richardson <root@localhost.localdomain>
wrote:

(snip)

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. 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

 

[Benj]

On Jun 17, 1:49 pm, RichD <r_delaney2...@yahoo.com> wrote:

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?

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!

 

[Szczepan Bialek]

"Phil Hobbs" <pcdhSpamMeSenseless@electrooptical.net> napisal w wiadomosci
news:4DFB9514.2010709@electrooptical.net...

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.).

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

 

[Szczepan Bialek]

"glen herrmannsfeldt" <gah@ugcs.caltech.edu> napisał w wiadomości
news:itggbe$8oj$2@dont-email.me...

In sci.physics.electromag huhie <invalid@invalid.invalid> wrote:

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

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

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).

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

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

Shorted ends are like a loop dipole.

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.

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

 

[Szczepan Bialek]

"Salmon Egg" <SalmonEgg@sbcglobal.net> napisał w wiadomości
news:SalmonEgg-6618A7.19323717062011@news60.forteinc.com...

In article
f8b96838-84f7-4e19-b352-f470595ebeb8@k15g2000pri.googlegroups.com>,
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.

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*

..

 

[krw@att.bizzzzzzzzzzzz]

On Fri, 17 Jun 2011 20:30:09 -0700, "Don Kelly" <dhky@shawcross.ca> wrote:

"glen herrmannsfeldt" wrote in message news:itga9f$9o4$2@dont-email.me...

In sci.physics.electromag Chris Richardson <root@localhost.localdomain
wrote:

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

What is the dual of the electron? (Magnetic monopole?)