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