MaplePrimes - answers and comments on Question, Kirchhoff and linear systems

Circuit solver

Joe Riel — Sat, 18 Oct 2008 22:32:24 Z

You might check out the Syrup package in the application center; it can quickly solve this circuit.

My bad

Sam9530130 — Sat, 18 Oct 2008 22:35:42 Z

I forgot to mention I need to solve this using a linear system.

I've been reading about

Sam9530130 — Sat, 18 Oct 2008 23:56:50 Z

View 6892_Kirchhoff.mw on MapleNet or Download 6892_Kirchhoff.mw
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I've been reading about it since this morning. I made a linear system using only Kirchhoff's Current Law. ( The current entering a junction is equal to the current leaving it )
But I don't see how I will get to use the Voltage law yet.
Also when I solve the system, it gives me that I₉=0.

edit : Would it be good if I started at either V₁ or V₂ and I'd do 9 different ways and come back at the starting point. I'd have equations that would look like this : V₂ - R₁₀*I₉ - R₂*I₃ = V₁
or something like that.

Am I in the good way or I didn't understand the concept?

Put aside this circuit for a while

jakubi — Sun, 19 Oct 2008 00:52:55 Z

Begin with simpler circuits, of one or two loops. You have two basic standard methods for writing the system of equations: by branch current and by mesh current. Besides your textbooks, you may find by googling for these methods plenty of tutorials. Just as a sample I have found these ones:

http://www.allaboutcircuits.com/vol_1/chpt_10/2.html

http://www.allaboutcircuits.com/vol_1/chpt_10/3.html

mesh analysis

Joe Riel — Sun, 19 Oct 2008 00:53:30 Z

I'd use a mesh analysis, that requires only four equations:

eqs := {NULL
        , R2*M1 + R1*(M1-M2) + R3*(M1-M3)
        , R1*(M2-M1) + V1 + R5*M2 + R6*(M2-M4) + R4*(M2-M3)
        , R3*(M3-M1) + R4*(M3-M2) + R7*(M3-M4) - V2 +R10*M3
        , R6*(M4-M2) + R8*M4 + R9*M4 + R7*(M4-M3)
       };

sol := solve(eqs,{M1,M2,M3,M4});

To solve for a particular current in a branch, express it in terms of the meshes. For example,

I5 = M3 - M2:

To get numerical values, create a set of equations for the parameters, and substitute them in, along with the solution:

params := {R1 = 5, R2 = 200, ... }:
subs(sol, params, M3-M2);

an advise

jakubi — Sat, 18 Oct 2008 22:56:46 Z

If you do not know yet what Kirchhoff laws are, it seems prudent that you learn them reading your textbook of Electricity and Magnetism and then begin solving simpler circuits.