resistors and capacitors in series and paralell...

[Hal]

Wow in physics the other day we derived the formula to find the total capacatince of 2 caps in paralell and series, then I went ahead and did it for resistors...I actually understand this now.  Its pretty sick, the theory...instead of just blindly knowing that resistors add values in series...I get it!   :twisted:      :twisted:

[Hal]

okay I gotta share its burning inside me!

for capacitors in parallell (i can never spell that):


the basic defenition of capacitance says:
C=Q/V, where c is Capacitance in farads, Q is charge in Couloumbs and V is voltage (in volts).


since both leads toutch the same potential, they have the same voltage drop across them...

Vt=V1=V2

now, since when once charge flows into one side of a capacitor, it pushes one out of hte other side...and the charge on each plate remains equal and opposite, we can say:

Qt=Q1+Q2

which says pretty much that the total charge leaving the source of potential equals the charge on on a single plate of each of the capacitors...

take that and divide by voltage...

Qt/Vt=Q1/V1+Q2/V2

and substitute using the first forumla...

Ct=C1+c2
yay!

Next: series!

okay the principles get a little more complicated here...

Kirschoff's second principle says that the sum of all potential drops adds up to the source potential. Which means that for 2 caps in series...

Vf=V1+V2

okay...now for the hard part....pretty much charge doesn't flow between the plates of a capcitor...it is induced to flow from the charged plate...so take 2 in series...one electron leaves the battery, jumps to the top plate...that repells one electron to leave the bottom plate, which travels to the second capacitor, which sends an electron of its bottom plate to the battery...

- |
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+ |
   |
- |
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+ |

so pretty much what this means is that the total charges on each capacitor has to be equal, since for one charge to enter the circuit, it has to laeave the other side...

Qt=Q1=Q2

this time take voltage and divide by charge...

Vt/Qt=V1/Q1+V2/Q2

take the initial formula, and invert it.... C=Q/V, 1/C=V/Q

and substitute 1/Ct=1/C1+1/C2

okay resistors...I think more people are familliar with the principles for these...

resistors in series:
basic defenition - ohm's law.  R = V/I

Kirshoff's first principle:  The sum of currents flowing into a junction = the sum of currents flowing out of a junction.

It=I1=I2

Kirchoff's second principle: Stated above...

Vt=V1+V2

divide by I
Vt/It=V1/I1+V2/I2
substitute using Ohm's Law....

Rt=R1+R2

paralell -
once again the leads toutch the same potential...

Vt=V1=V2

and kirchoff's first principle...

It=I1+I2

invert Ohm's Law... 1/R=I/V

It/Vt=I1/V1+I2/V2

1/Rt=1/R1+1/R2


all done :-D

[Transmogrifox]

Excellent  I think it helps a lot of people here when somebody lays it out like that.  These things seem simple to us who have been doing it for quite a few years, but I remember before deciding to study electrical engineering, I couldn't even read a schematic.  I wanted to build a Fuzz pedal but I had no idea of how it worked, or even that the resistor with an arrow in the middle is a pot...

People like me then are the people who can benefit greatly from this forum and posts like that...

[petemoore]

There are myriad application examples of how an opamp works different biasing setups, etc.
 I know I've gathered alot of info and I keep studying it, but these equations only give me a glimpse of the sense they make, enough of a glimpse to understand this part and that part a little bit, and to know that
better comprehension of the equations would open up a whole new area of information to process.
 If there were case in point type examples [like there arent't] but in one lplace depicting equations that are relevant to setting up OA's...so that a 'street' guy like me can start to decipher...
 It could be that it's all just too much for me to sort out, or I haven't found the right page to re- study yet.