Sunday 17 February 2013
MESH ANALYSIS
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MESH ANALYSIS
The mesh analysis is a
systematic way of applying KVL around each mesh of a circuit and describes the
branch voltages in terms of the mesh currents. This will give us a set of
equations that we solve together to find the mesh currents. Once we find the
mesh currents we can use them to calculate any other currents or voltages of
interest.
EXAMPLE
In the above circuit find ix
RULES TO BE FOLLOWED
1) Find number of loops and
mark loop directions in clockwise.
2) Take individual loops and
mark the polarities according to current direction you have taken.
3) Apply KVL to the
individual loops
SOLUTION
Step 1 : there are 2 loops
in the given circuit and marking current directions in clockwise direction
FOR LOOP
1
While applying KVL consider
I1 > I2
Mark the polarities
according to the loop current
Apply KVL to loop 1
7 – (1 * I1) – (2
* ( I1 - I2)) – 6 = 0
3 I1 – 2 I2
= 1
----------------------------------------( 1 )
FOR LOOP2
While applying KVL consider
I2 > I1
Mark the polarities
according to the loop current
-3 * I2 – 4 * I2
– 9 + 6 – 2 * ( I2 – I1 ) = 0
2 I1 – 9 I2
= 3
-------------------------------------------- ( 2 )
Solving equation 1 and 2 we
get
Multiplying eq 1 with 2 6I1 – 4 I2 = 2
Multiplying eq 2 with 3 6I1 – 27 I2 = 9
- + -
-------------------------
-------------------------
0 23 I2 = - 7
I2 = - 7 / 23
Substituting the value
of I2 in eq 1 we get I1
= 3 / 23
By using calculator
Go to press mode button
Then press 5: EQN
Then press 1 : anX + bnY
= cn
then
enter values
At node A
At node A
Applying KCL
I1 is incoming
current,I2 & ix are out going currents
-I1+ I2
+ix = 0
ix = I1
– I2
substituting the values of I1
& I2 we get
ix = 10 / 23
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