circuit/mesh analysis

[qwex]

I'm in an intro to electrical engineering class, and our textbook is downright unhelpful...it doesn't explain things very well, if at all, and I'm having trouble figuring out this mesh analysis stuff. we're given a small, 3 loop circuit and have to find the 3 currents in each loop using the voltage and current laws...anyone know of a good tutorial or something on this stuff somewhere? I get the overall theory, but I'm just not sure how these circuits can and cannot work, e.g. does the current start from the battery, does the current split or not at this node, etc. I'm going to try to see the professor today, but it doesn't help that I have class when he has office hours, and I doubt he'll be able to clarify more then he does in class...thanks in advance

 

[rimshaker]

Just read as many intro. to EE textbooks as you can, don't just rely on a single textbook. The further you go into the EE curriculum, you'll be wishing mesh and nodal analysis was all there is to circuits 🙂 Yes, current starts at the battery (+), but also ends there as well (-). You have to picture current as being present throughout the circuit at all times.

 

[qwex]

yeah, the "current is everywhere always" idea is confusing me. but in examples we've done in class, the current goes the opposite way through the battery, which we were told means the battery is being charged. I'm also wondering how at some resistors to know which current is going through it, if it's part of 2 loops, for example.

 

[Elledan]

<< current starts at the battery (+), but also ends there as well (-). >>

Actually, the electrons which make up the current travel in exactly the opposite direction (- to +) 🙂

*ducks and runs*

 

[rimshaker]

<< Actually, the electrons which make up the current travel in exactly the opposite direction (- to +) 🙂

*ducks and runs* >>



Come on now.. I'm referring to just simple current for qwex, not device phyics. Besides, i'm sure he knew that.... 🙂

 

[Eskimo]

You might try this site out.

Try some of the experiments and they'll let you see the effect of increasing resistances and voltages, although they won't teach you the math that well.

 

[EmMayEx]

What helps is to realize that you only need to remember 2 things:

1. The sum of the current entering all nodes is zero. (Kirchhoff's current law)
2. The sum of the voltage drops around all closed loops is zero. (Kirchhoff's voltage law)

Using this you should be able to write down enough independant equations to be able to solve for the unknown currents and voltages. You can use the device equations (I = E/R for a resistor for a linear or "non energy storing" circuit) to give you eqations that relate voltage across a leg to the current through it.

When you get to circuits with energy storage devices (capacitors and inductors) the same two rules apply but with a twist. The sum is now defined as the sum of the complex (time varying) currents and voltages which are represented as complex numbers (1+3i or 1+3j for EE's were i = j = the square root of -1). The rules for adding, and multiplying complex numbers are slightly more complicated than real numbers but the concept is identical.

For small systems, you can systematically go through and write an current summation equation for every node and a loop equation for every possible loop and a device equation for every resistor and then solve all of these simultaneously using matrix algebra. In fact that is what most electrical network simulation packages do, using complex aritmetic for non linear devices like capacitors and inductors. If you are solving the equations by hand you probably have a small enough system to write down all the possible equations and substitue numbers for all the know voltages and currents. You can then either simply the set of equations by substituting them into one another until you can solve for an unknown or put the coefficients in a matrix and use gaussian elimination to solve all the unknowns.

As with word problems the trick is writing all the possible equations down (finding all the possible loops can be a trick), simplifying and rearraging things and solving for one of the unknowns.

As for knowing how current "knows" which way to flow through a resistor, it always flows from higher potential to lower potential (convention current that is, as someone pointed out electron current flow the opposite way but this is just a matter of which end of the battery they decided to call + a few hundred years ago). You can't guess what direction the flow is until you solve for the voltages at the nodes. Typically you are given just enough information to solve the system which means you have to write a system of equations to figure it probably won't be obvious what the current flow is by inspection (unless you've solved a similar problem before).

Hope this helps, network calculations were never my favorite pastime either.

Max L.

 

[highwire]

Sometimes in practice, it's good to just do the Kirchoff thing and grind out the solution.

At other times, it may be possible and an advantage to get an impedance feel for the circuit by solving it using our old friend Thevenin's important theorem.

In a typical case with 3 legs, 2 of the legs can often be easily solved if the 3rd is disconnected. After solving the first 2 legs, replace it with its Thevenin equivalent. Now, hook up the 3rd leg again. It will now be a single loop. Just apply ohm's law and the whole problem resolves.

Here is a link to a Thevenin page:

quick tutorial

 

[blahblah99]

Also remember:

If you know the voltage between two points of an element, you can find the current through it regardless of what's connected to it (ie, current source, more elements, etc etc)
and if you know current THROUGH the element, you can find the voltage. Those two are just simple applications of V=IR.


to clarify a little more on kirchoff's laws,

1. The sum of the current entering all nodes is zero. (Kirchhoff's current law)

You mean sum of all currents entering AND leaving a node is zero... ie, what goes in, must come out.

2. The sum of the voltage drops around all closed loops is zero. (Kirchhoff's voltage law)

You can pick any closed loop and specify a direction. Pick a current direction also. Then just walk around the loop adding up the voltages.
Usually you will end up with a system of x equations with x unknowns and you will have to solve for it.

To get better at this stuff, you need to practice practice and practice. This just involves RLC. Wait till you get to AC, laplace transform, bode plots, diodes, bjts, mos, differential amp, small signal analysis, current sources, feedback, frequency compsentation, stability, and multistage amps. Now that is where all the fun is.😉🙂