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Re: [Phys-L] standard dc circuits



On 11/22/2013 12:11 PM, Paul Lulai wrote:

If all wires are of the same material, diameter, length (and so on)
why is the current less in the parallel branches than in the wires
before and after the parallel branch?

Well, what matters is not "diameter" but rather area,
and in the parallel part of the circuit there is
twice as much area, because of the two branches in
parallel.

Also, it isn't even the properties of the hookup wires
that matters, but rather the properties of the resistive
element within each light bulb.

You could double or halve the diameter of the hookup wire
and it wouldn't significantly change the outcome. If this
is obvious, fine. If it is non-obvious, consider the fact
that the voltage-divider law (derived from Ohm's law) is
*nonlinear*.

For easy numbers, if 1 amp flows through the first lamp, then 0.5
amps flow through each lamp in parallel

That is the "constant current" approach. That's not the
easy way to attack this problem (although it works great
for lots of /other/ problems).

Suppose there is just one battery. It imposes a voltage
on the resistor. The electrons flow through the resistor,
scattering off various obstacles, bing-bong-bang, in such
a way that the current depends on the driving voltage ...
and on the inverse resistance. This gives us a microscopic
basis for understanding Ohm's law. All the macroscopic
behavior of the voltage divider and current divider follows
from Ohm's law.

The lesser current in the parallel R||R part of the circuit
is associated with a lesser voltage drop across that part
of the circuit. If we didn't have this lesser voltage,
too much current would flow. Enough charge would build
up (*) on the node between the parallel part and the
series part. This charge is not very big in absolute
terms, but it is just enough to change the fields, to
change the voltages. The node-voltage changes in the
"correct" direction and keeps changing until the voltages
come into compliance with Ohm's law.

Note (*) yes, this charge buildup is a clear violation
of Kirchhoff's current law. There is no /long term/
steady rate of charge buildup, but there definitely is
a startup transient when you first hook up the circuit.

The batteries produce a field that move charges

The battery (approximately) dictates the voltage on
its terminals. At each place in the world, the local
field is dictated by /all/ the charges, not just the
battery. A small charge up close can have a bigger
effect than a large charge far away.

The little non-Kirchhoff charges are easy to overlook,
but they are key to constructing a microscopic explanation
of what's going on in an electrical circuit.

Note that I am a bit skeptical of the wisdom of spending
time on the /microscopic/ description of circuits in the
introductory course. It's not something most people
need to know. *I* think the microscopic physics is
nifty ... but this isn't about me. We should do what's
best for the students. For 99% of electrical engineering
and 99.99% of life in general, the phenomenological
macroscopic approach -- Ohm's law -- is just fine.

IMHO the motto of the physics course (and lots of
other things besides) should be "Let me teach you the
easy way to solve interesting and important problems."
There are lots of such things and lots of demands on
our time, so let's stay focused. Microscopic steering
charges are *not* the easy or smart way to solve
ordinary circuit problems.