Today we've advanced a little more in theory, rest of the time it was individual work on projects (mine and Ahuva's is going to be called fluteduino before we're settled with the name and the hardware).
We started off by being introduced to the Parallel Resistors topic. Yep, it's been proved that in this case the total resistance of the two resistors is going to be not more but less than that of any of the individual resistors involved (except in case that one of the resistors has no resistance at all). Or to be more specific:
Rtotal = R1*R2/(R1+R2)
The initial study plan, as it turned out, did not list the act of proving this theorem, so it was more like an impulse of the moment. Which I think was a good impulse, as it made us all feel much more secure and demistified. Watch, it's a pretty straightforward and, dare I say, elegant one:
From Ohm's Law we know that:
Vtotal=Itotal*Rtotal.
(
Vt=It*Rt)
So,
Rt=Vt/It
But also:
Vt=I1*R1
And (as resistors are connected in parallel):
Vt=I2*R2
Hence,
I1=Vt/R1
I2=Vt/R2
Regarding It, it's simply a sum of I1 and I2, because the total current (call it a "flow") cannot be any more or less than the "subflows" strictly derived of it (Kirchoff Law):
It=I1+I2
Hence,
It=Vt/R1+Vt/R2
Going back and subsituting, we get:
Rt=Vt / (Vt/R1 + Vt/R2)
Simplify this a little and we're done:
Rt = R1*R2 / (R1+R2)
All of that and more, with charming pictures and classic diagrams, should be found in Nori's Lecture notes.
See you tomorrow morning,
Anton.
