Mesh Current Method
The mesh current method is deduced from the Kirchhoff�s voltage law (KVL) and
superposition theorem.
The following formulas are used to solve circuit.
where
 Loop
i resistance is the sum of resistances of all branches
which contain in the given loop.
 Loop
i to Loop j resistance. If the directions of
loops are opposite then resistance is negative.
Otherwise, it's positive. The value equals the sum of branches
resistances of all branches, which contains in both
loops.
Loop i � EMF
Number of loop equations equal number of KVL equations.
Loop Number = Branch Number �(Nodes Number �1) � Current sources Number
If the circuit contain current sources it is
necessary to create additional loops. Branch with current source can be contained
in one loop.
Sample: Circuit Solution By Mesh Current
Step 1. Construct circuit using AKNM Circuit Magic
Electrical scheme
Initial variables
R1=10Ohm; R2=20Ohm;
R3=25Ohm; R4=10Ohm;
R5=10Ohm;
E1=10V; E2=15V;
J1=10A;
Solution
I11�R11+I22�R12+I33�R13=E11
I11�R21+I22�R22+I33�R23=E22
(Loop 1 Resistance)
R11=R2+R5+R1=40
(Loop 1 to loop 2 Resistance is the sum of branch 1 and branch2 resistances.
The resistance is positive due non-opposite Loop1 � Loop3 directions)
R12=R2+R5=30
R13=R2=20
R21=R2+R5=30
R22=R2+R5+R3+R4=65
R23=R2+R4=30
E11= -E2-I33�R31=-215
E22= E1-I33�R32=-290
40I11+30I22=-215
30I11+65I22=-290
I11=-3,102941
I22=-3,029412
I33=10
I1= I11+I22+I33=3,8676471
I2= I11+I22=-6,1323529
I3=-I11=3,1029412
I4= J1=10
I5= I22=-3,0294118
I6=-I22-I33=-6,9705882
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