Mesh Current circuit analysis method. Mesh Current circuit analysis using Circuit-Magic
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Mesh Current Method

The mesh current method is deduced from the Kirchhoffs 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

I11R11+I22R12+I33R13=E11

I11R21+I22R22+I33R23=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-I33R31=-215

E22= E1-I33R32=-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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