On Jul 6, 7:27*pm, Keith Dysart wrote:
Then contrast those two laws with the previously discussed
power (rate of flow of energy) and 'conservation of energy'
law. You should be able to discern the similarities.

Of course, the similarities are so obvious I don't even need to state
them. Why are they not obvious to you?

There is a principle of conservation of energy. There is no principle
of conservation of energy flow (power). All you have to do to destroy
power is stop the flow of energy. All you have to do to create power
is to start the flow of energy.

There is a principle of conservation of charge. There is no principle
of conservation of charge flow (current). All you have to do to
destroy current is stop the flow of charges. All you have to do to
create current is to start the flow of charges.
--
73, Cecil, w5dxp.com

On Jul 6, 10:59*pm, Cecil Moore wrote:
On Jul 6, 7:27*pm, Keith Dysart wrote:

Then contrast those two laws with the previously discussed
power (rate of flow of energy) and 'conservation of energy'
law. You should be able to discern the similarities.

Of course, the similarities are so obvious I don't even need to state
them.

Good. You have made some progress then...

There is a principle of conservation of energy. There is no principle
of conservation of energy flow (power). All you have to do to destroy
power is stop the flow of energy. All you have to do to create power
is to start the flow of energy.

There is a principle of conservation of charge. There is no principle
of conservation of charge flow (current). All you have to do to
destroy current is stop the flow of charges. All you have to do to
create current is to start the flow of charges.

and partially contrasted the two. But you did not show how Kirchoff's
current law derives from conservation of charge.

Still, you have made some progress, so I will try again with showing
the derivation, though this time with charge and current.

Conservation of charge requires that:
the charge added to a region
- the charge removed from a region
equals
the charge originally in the region
+ the increase of charge stored in the region

When the charge can be described with functions of time, we can write:

Qin(t) - Qout(t) = Qoriginal + Qstored(t)

Differentiating we obtain

Qin(t)/dt - Qout(t)/dt = 0 + Qstored(t)/dt

At a junction, where charge can not be stored, this reduces to

Qin(t)/dt - Qout(t)/dt = 0

Alternatively

Qin(t)/dt = Qout(t)/dt

Recognizing that Q(t)/dt is charge flow per unit time or current
we obtain Kirchoff's current law, colloquially: the current flowing
in to a junction equals the current flowing out of a junction.

I leave it to you to do the similar derivation for energy, based
on conservation of energy. The result will be

EnergyIn(t)/dt = EnergyOut(t)/dt

And similar to Kirchoff, this applies at a juncion, a place where
energy can not be stored.

Of course Energy(t)/dt is just a mathematical expression of energy
flow or power, so we obtain

PowerIn(t) = PowerOut(t) (at a junction)

But don't beleive me. Do the derivation yourself. You can pattern
your derivation on the one above for Kirchoff.

I'd go on to show how my analysis of your circuit carefully
picked junctions that could not store energy, but I have found
it better to educate one step at a time. So we can do that
later.

....Keith

Keith Dysart wrote:
current law derives from conservation of charge.

Still, you have made some progress, so I will try again with showing
the derivation, though this time with charge and current.

Conservation of charge requires that:
the charge added to a region
- the charge removed from a region
equals
the charge originally in the region
+ the increase of charge stored in the region

When the charge can be described with functions of time, we can write:

Qin(t) - Qout(t) = Qoriginal + Qstored(t)

Differentiating we obtain

Qin(t)/dt - Qout(t)/dt = 0 + Qstored(t)/dt

At a junction, where charge can not be stored, this reduces to

Qin(t)/dt - Qout(t)/dt = 0

Alternatively

Qin(t)/dt = Qout(t)/dt

Recognizing that Q(t)/dt is charge flow per unit time or current
we obtain Kirchoff's current law, colloquially: the current flowing
in to a junction equals the current flowing out of a junction.

I leave it to you to do the similar derivation for energy, based
on conservation of energy. The result will be

EnergyIn(t)/dt = EnergyOut(t)/dt

And similar to Kirchoff, this applies at a juncion, a place where
energy can not be stored.

Of course Energy(t)/dt is just a mathematical expression of energy
flow or power, so we obtain

PowerIn(t) = PowerOut(t) (at a junction)

But don't beleive me. Do the derivation yourself. You can pattern
your derivation on the one above for Kirchoff.

I'd go on to show how my analysis of your circuit carefully
picked junctions that could not store energy, but I have found
it better to educate one step at a time. So we can do that
later.

...Keith


How do you define energy of a node without reference to another node.
How is it measured?

On Jul 7, 8:05*am, joe wrote:
Keith Dysart wrote:

current law derives from conservation of charge.







Still, you have made some progress, so I will try again with showing
the derivation, though this time with charge and current.

Conservation of charge requires that:
* the charge added to a region
* - the charge removed from a region
* equals
* the charge originally in the region
* + the increase of charge stored in the region

When the charge can be described with functions of time, we can write:

* Qin(t) - Qout(t) = Qoriginal + Qstored(t)

Differentiating we obtain

* *Qin(t)/dt - Qout(t)/dt = 0 + Qstored(t)/dt

At a junction, where charge can not be stored, this reduces to

* *Qin(t)/dt - Qout(t)/dt = 0

Alternatively

* *Qin(t)/dt = Qout(t)/dt

Recognizing that Q(t)/dt is charge flow per unit time or current
we obtain Kirchoff's current law, colloquially: the current flowing
in to a junction equals the current flowing out of a junction.

I leave it to you to do the similar derivation for energy, based
on conservation of energy. The result will be

* *EnergyIn(t)/dt = EnergyOut(t)/dt

And similar to Kirchoff, this applies at a juncion, a place where
energy can not be stored.

Of course Energy(t)/dt is just a mathematical expression of energy
flow or power, so we obtain

* *PowerIn(t) = PowerOut(t) * *(at a junction)

But don't beleive me. Do the derivation yourself. You can pattern
your derivation on the one above for Kirchoff.

I'd go on to show how my analysis of your circuit carefully
picked junctions that could not store energy, but I have found
it better to educate one step at a time. So we can do that
later.

...Keith

How do you define energy of a node without reference to another node.
How is it measured

I am sorry, I do not understand the question. Can you provide a bit
more context, or perhaps a representative example?

....Keith

Keith Dysart wrote:
On Jul 7, 8:05 am, joe wrote:
Keith Dysart wrote:

current law derives from conservation of charge.







Still, you have made some progress, so I will try again with showing
the derivation, though this time with charge and current.
Conservation of charge requires that:
the charge added to a region
- the charge removed from a region
equals
the charge originally in the region
+ the increase of charge stored in the region
When the charge can be described with functions of time, we can write:
Qin(t) - Qout(t) = Qoriginal + Qstored(t)
Differentiating we obtain
Qin(t)/dt - Qout(t)/dt = 0 + Qstored(t)/dt
At a junction, where charge can not be stored, this reduces to
Qin(t)/dt - Qout(t)/dt = 0
Alternatively
Qin(t)/dt = Qout(t)/dt
Recognizing that Q(t)/dt is charge flow per unit time or current
we obtain Kirchoff's current law, colloquially: the current flowing
in to a junction equals the current flowing out of a junction.
I leave it to you to do the similar derivation for energy, based
on conservation of energy. The result will be
EnergyIn(t)/dt = EnergyOut(t)/dt
And similar to Kirchoff, this applies at a juncion, a place where
energy can not be stored.
Of course Energy(t)/dt is just a mathematical expression of energy
flow or power, so we obtain
PowerIn(t) = PowerOut(t) (at a junction)
But don't beleive me. Do the derivation yourself. You can pattern
your derivation on the one above for Kirchoff.
I'd go on to show how my analysis of your circuit carefully
picked junctions that could not store energy, but I have found
it better to educate one step at a time. So we can do that
later.
...Keith
How do you define energy of a node without reference to another node.
How is it measured

I am sorry, I do not understand the question. Can you provide a bit
more context, or perhaps a representative example?

...Keith


Sure. You described charge flow in and out of an isolated node with no
need to reference any other node or part of the circuit. Then you say
the same thing can be defined for energy. However, how is energy defined
in terms that only refer to characteristics of the node without
involving any other part of the circuit or other nodes.

On Jul 7, 9:36*pm, joe wrote:
Keith Dysart wrote:
On Jul 7, 8:05 am, joe wrote:
Keith Dysart wrote:

current law derives from conservation of charge.

Still, you have made some progress, so I will try again with showing
the derivation, though this time with charge and current.
Conservation of charge requires that:
* the charge added to a region
* - the charge removed from a region
* equals
* the charge originally in the region
* + the increase of charge stored in the region
When the charge can be described with functions of time, we can write:
* Qin(t) - Qout(t) = Qoriginal + Qstored(t)
Differentiating we obtain
* *Qin(t)/dt - Qout(t)/dt = 0 + Qstored(t)/dt
At a junction, where charge can not be stored, this reduces to
* *Qin(t)/dt - Qout(t)/dt = 0
Alternatively
* *Qin(t)/dt = Qout(t)/dt
Recognizing that Q(t)/dt is charge flow per unit time or current
we obtain Kirchoff's current law, colloquially: the current flowing
in to a junction equals the current flowing out of a junction.
I leave it to you to do the similar derivation for energy, based
on conservation of energy. The result will be
* *EnergyIn(t)/dt = EnergyOut(t)/dt
And similar to Kirchoff, this applies at a juncion, a place where
energy can not be stored.
Of course Energy(t)/dt is just a mathematical expression of energy
flow or power, so we obtain
* *PowerIn(t) = PowerOut(t) * *(at a junction)
But don't beleive me. Do the derivation yourself. You can pattern
your derivation on the one above for Kirchoff.
I'd go on to show how my analysis of your circuit carefully
picked junctions that could not store energy, but I have found
it better to educate one step at a time. So we can do that
later.
...Keith
How do you define energy of a node without reference to another node.
How is it measured

I am sorry, I do not understand the question. Can you provide a bit
more context, or perhaps a representative example?

...Keith

Sure. You described charge flow in and out of an isolated node with no
need to reference any other node or part of the circuit. Then you say
the same thing can be defined for energy. However, how is energy defined
in terms that only refer to characteristics of the node without
involving any other part of the circuit or other nodes.

Perhaps some examples will help.

Consider the output terminals of a generator to be junction. Then the
power delivered from the generator to the junction must exactly equal,
at all times, the power taken from the junction by the load, since
there is no storage in the junction.

It should be noted that the 'junctions' used for a power analysis
are not the same as the junctions used in Kirchoff's current
law. The concepts are analogous, not identical.

Another example. In the simple Thevenin generator, the power provided
by the voltage source must exactly equal, at all times, the power
taken by the resistor plus the power taken by the load. In this
example, it is difficult (impossible?) to identify a physical
'junction' where the power must balance, yet the notion is still
applicable.

....Keith

On Jul 8, 6:04*am, Keith Dysart wrote:
Consider the output terminals of a generator to be junction. Then the
power delivered from the generator to the junction must exactly equal,
at all times, the power taken from the junction by the load, since
there is no storage in the junction.

I will leave you with this parting thought. All that you are saying is
that the power at one point (special case: away from any energy
storage device) is the same as the power at another point in the same
wire (special case: an infinitesimal distance away). No rational
person would argue with you on that point. However, that is NOT a
general case and in no way proves that power is conserved in general.
It is simply a special case where there is a one-to-one correspondence
between energy and power, something I pointed out earlier.

The throw of a switch can cause power to be created or destroyed. The
throw of a switch cannot cause energy to be created or destroyed.
That's the basic conceptual difference between power and energy that
you are missing. The same thing is true for current vs charge.

In my energy articles, I took advantage of the special case of one-to-
one correspondence between average energy and average power. You
neglected to do that for your instantaneous power calculations and
proved beyond any doubt that power is not conserved. Your own
continuity equation posting indicated that you had erroneously omitted
something important from your previous calculations.
--
See y'all later, 73, Cecil, w5dxp.com

Keith Dysart wrote:

Perhaps some examples will help.

Consider the output terminals of a generator to be junction. Then the
power delivered from the generator to the junction must exactly equal,
at all times, the power taken from the junction by the load, since
there is no storage in the junction.

It should be noted that the 'junctions' used for a power analysis
are not the same as the junctions used in Kirchoff's current
law. The concepts are analogous, not identical.

Another example. In the simple Thevenin generator, the power provided
by the voltage source must exactly equal, at all times, the power
taken by the resistor plus the power taken by the load. In this
example, it is difficult (impossible?) to identify a physical
'junction' where the power must balance, yet the notion is still
applicable.

...Keith

It sounds like your "junction" for energy analysis is what's called a
"port" in RF analysis. If so, it would be less confusing for you to use
that term, since "junction" has a different established meaning in
circuit analysis.

Roy Lewallen, W7EL

On Jul 7, 6:04*am, Keith Dysart wrote:
At a junction, where charge can not be stored, this reduces to

Sorry, your examples are irrelevant to the technical fact that there
is no conservation of current principle because charge can be stored.
Until you can prove a conservation of current principle, you are
wasting my time.
--
73, Cecil, w5dxp.com

"Cecil Moore" wrote
...
On Jul 7, 6:04 am, Keith Dysart wrote:
At a junction, where charge can not be stored, this reduces to

Sorry, your examples are irrelevant to the technical fact that there
is no conservation of current principle because charge can be stored.

In EM current is incompressible. EM is older then electrons.
"charge can be stored" apply to electrons. It is impossible to marry EM and
electrons.

Until you can prove a conservation of current principle, you are
wasting my time.

"According to theory" a conservation of current principle (continuity
equation) is the assumption.

In EM is the displacement current in solid insulators (also in vacuum). It
is always incompressible because the motions of the particles are
synchronized (charges can not be gathered).

EM is beautiful but useles in techniques. It is useful to teach the math.
S*
--
73, Cecil, w5dxp.com