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Re: [Phys-l] Kirchhoff's laws, or not



If any given Kirchhoff Node is small enough that it's self capacitance is negligible (a not unreasonable condition) then it will not build up enough charge to violate the Current Rule.

The idea of an arbitrarily small 'node' does not seem extreme.
(Circuit board designers need to be aware of the shortcomings of their media).)

It DOES seem a bit odd to consider a helicopter to be a circuit 'node'.

Kirchhoff's RULES seem better than Kirchhoff's LAWS.
(I always taught Ohm's Rule of Thumb instead of Ohm's Law.)


At 1:14 PM -0700 7/7/10, John Denker wrote:
On 07/07/2010 12:37 PM, chuck britton wrote:

If a Kirchhoff 'node' is small enough - is the 'law' ok?

No, not OK.

Consider the example from yesterday: The current into
the helicopter was on the order of 30 mA, of which 30 mA
violated Kirchoff's law. If you break the helicopter
into 1000 sub-nodes, then roughly speaking each one gets
30 É A of which 30 É A violates Kirchhoff's law.

It's a 100% violation either way.

(Conservation of Charge?)

Conservation of charge is good physics.
Kirchhoff's law, not so much.

K's law assumes a lot more than conservation of charge.
Basically it assumes the self-capacitance is negligible.
++ Sometimes this is OK if the parasitic one-terminal
self-capacitance is dominated by an ordinary two-terminal
capacitor that you have designed into the circuit.
++ Sometimes this is OK in the low frequency limit,
frequency É÷ << 1/RC, if the self-capacitive impedance
1/iÉ÷C is dominated by some ordinary two-terminal
conductive component 1/R.
-- Neither of those provisos applies to the helicopter,
not even close. AFAICT the self-capacitance is basically
the whole story in the video we saw.

(There may be other stuff going on, such as corona
discharge from the rotor tips and from static wicks
on the airframe, but that is at most an Nth order
correction in this case. You might start to care
about this stuff when working on DC lines, but for
AC the self-capacitance is dominant.)


====================================

On 07/06/2010 02:57 PM, Stefan Jeglinski wrote:

If suit is faraday cage,

As previously mentioned, it's not just a Farady cage.

Here's another way to see this: The working of a Faraday
cage is independent of the shape of the cage. If the suit
were just a Faraday cage, the person could flail around
do anything he wanted. The elaborate choreography with
the probe and the clamps tells you there's a lot more
going on.

The Maxwell equations are linear. The equations for
breakdown and conductivity in the air are spectacularly
nonlinear. The procedure in the video makes heavy use
of this nonlinearity. I reckon the suit has /some/
value, but it cannot be considered the first line of
defense.
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