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Re: [Phys-L] standard dc circuits

I agree with what others have stated about the source of the potential differences. But I suspect your question is on a simpler level. Once it is determined that the voltage on the parallel pair is half that on the single resistor (when equilibrium has set in), then since Voltage is the integral of field over distance, the field must be half that of the single resistor.

As others have stated, the field is due to the surface charges. After the transients have died out, those charges must distribute themselves in such a way that current is a conserved quantity - but that current is given by conductivity multiplied by cross sectional area multiplied by field. The field and surface charges will hunt back and forth in value until equilibrium is established.

It is not unlike what happens to charges in a conductor when placed in a static field. Charges flow, polarization of charges occur, and the field fluctuates until an equilibrium occurs with a net zero field in the conductor.

Bob at PC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Paul Lulai
Sent: Friday, November 22, 2013 2:11 PM
To: Phys-L@Phys-L.org
Subject: [Phys-L] standard dc circuits

I have a question about the junction rule for simple dc circuits.
I have a battery connected to 1 lamp, then split to 2 lamps in parallel and back
to the battery.
For easy numbers, if 1 amp flows through the first lamp, then 0.5 amps flow
through each lamp in parallel (if all lamps are ideal).
Using the junction rule, I know that current into each junction or node must
equal the current out of each junction or node. It is simply a conservation of
charge in that area.
How does that reconcile with a fields approach? I might have some incorrect
notions below. I am open to correction.
The batteries produce a field that move charges already present in the wire.
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? Does something make the field in the parallel branches
smaller than the field in the series portion before and after the parallel
branch? I don't see it.
Thanks for any input.
Paul.

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