Kirchoff's Rules

[tweedclassic]

we just started DC circuit analysis in my physics class. Kirchhoff's rules (IE junction rule and loop rule) are very interesting. up to this point i have not come across a circuit i couldn't solve by breaking it up into series an parallel circuits.  as usual in physics i lean how little i really know.

how much do you end up using Kirchhoff's rules?
does it apply to AC circuits the same as DC circuits?


Cheers
R.

 

[PRR]

> i have not come across a circuit i couldn't solve by breaking it up into series an parallel circuits.

I "believe" the technique is universal.

And works as well for water-pipes and acoustics as for electricity.

But the number of computations increases exponentially with the number of loops.

Before computers, you could exact-solve several-loop problems, and exact-enough-solve many-loop problems IF you could make some simplifying approximations ("this part hardly matters").

I believe SPICE uses the same technique for networks of "any" size, limited by computational resources. (I can't check that because my student/trial SPICE has artificial net-size limits to make me buy the full-price edition.)

AC, DC, what's the difference? The electrons don't remember from one instant to the next. Reactances DO "remember", so AC computations must account for that, and are more complicated (and often complex).

If you really love Kirchhoff, get Kuehnel's Bassman 5F6-A http://pentodepress.com/home/books/bassman/
I analyze on the back of a napkin, so I approximate my butt off to find a rough answer. Kuehnel sets up full Kirchhoff equations, lines them up in a matrix, and uses some fancy-math to find the solution.

 

[livingnote]

Yeah, Kirchhoff for like 15 years had me going "huh what's that and what is it good for" and then I saw this guy:

http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-002Spring-2007/VideoLectures/detail/embed02.htm

Really cool

I have the same thing with water and general intuitive way of finding parallel associations that make pictures you can
grasp to understand stuff, it's so funny. I had this thing with voltage once where you have this ten-story building
and a metal ball, and the higher up you go on the stairs, the more "voltage" you have when you get ready to drop
the ball off a balcony, and now you have like resistance along the way down, as in, guys on the balconies below sticking
their heads out, and the more there are, the less each one gets konked in the noggin as it drops, and the degree of
"ouch" would be, like, watts. So, if you only have one guy on the lowest balcony, he gets killed, which would be
like, blowing up a component.

Not the very best model but it kinda made sense to me that way...

Or, like, in my heating there's that expansion chamber with a membrane that keeps water pressure nominal in the pipes,
like, there you have your rail capacitor...and of course valves and pumps and sandbags to obstruct it and propel it with...
the last apartment I was living in, the water pressure in the kitchen was way too low, I thought there wasn't enough
pressure in general, but turned out there was this way thin little pipe connecting the faucet to the main pipe, which was
kinda like "too much resistance".

I have this PCB thing too that there you have basically one big crazy "adventure island" water slide for the electrons.

One thing that had me bothered for a long time was the "fuse effect" of what happens when you melt your cable but it's
not an ohmic dissipation, and I had trouble understanding that one until I imagined a highway, where normally all the
cars are doing 55 MPH, but you get too many cars, in the case of electrons, instead of putting on their brakes and
causing a traffic jam, they all don't have any brakes, so they cause this massive carambolage because they all wanna
get to work on time.

So, the more evil their boss is, the more they'll wanna hit the gas, like, "more volts" and so "more current", and you
regulate that with resistances like stoplights and speed limits or speed bumps, causing power dissipation ("road rage").

 

[JohnRoberts]

Kirchoff rulz....  ;D

JR

 

[xmvlk]

how much do you end up using Kirchhoff's rules?

How many of Kirchhoff rules do You need? 2,3,or 4 ?
I use only that fourth.  ;D
ieeexplore.ieee.org/iel5/8148/23605/01086427.pdf?arnumber=1086427

 

[PRR]

> when you melt your cable but it's not an ohmic dissipation

Yes it is.

Car, car battery, car-wire, #22 jumper-leads, car radio.

Well, a clip fell off "+" and hit ground.

Several feet of car wire: about 0.015 ohms.

One foot thin jumper: also about 0.015 ohms.

Total 0.03 ohms.

12V battery.

Current is 12/0.03 = 400 Amperes.

400 amperes in one foot jumper drops 400*0.015 = 6V.

6V and 400 Amps is 2,400 Watts.

The wire has thermal mass, but not much.

The area to dissipate heat to air is about 0.08" circumference times 12" length or one square inch.

One Watt in one square inch makes about 100 deg C temp rise.

2,400 watts in one square inch makes 240,000 deg C temperature rise.

Actually, copper melts at 1,100 deg C. It still conducts, and glows incandescently, but falls-apart, leaving small burns on the carpet.

---
I've neglected a few things. The battery won't hold full 12V at 400A, maybe only 10V. Skinny wire cools better than flat heatsinks. By 1,000 deg C the radiation overwhelms the simple convention my rule of thumb is based on. So it's maybe only aiming at 50,000 deg C when it falls-apart at 1,100 deg C.

 

[livingnote]

Ah looky there, ohmic after all...thanks.

Whew, does simplify understanding considerably...it's pretty amazing how far logic
can self-deceive when your premise isn't right...

 

[Futureman]

Kirchoff rulz....  ;D

JR

It's not well known that his first name was 'Han' lol.

 

[boji]

Obi-Wan Kirchhoff certainly helps you learn to use the force.