


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 nonopposite 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= E2I33·R31=215
E22= E1I33·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=I22I33=6,9705882
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