MESH ANALYSIS IN AC CIRCUIT

MESH ANALYSIS

Kirchhoff's voltage law (KVL) forms the basis of mesh analysis. We must keep in our mind that the very nature of using mesh analysis is that it is to be applied to planar circuits.

EXAMPLE:

Determine current Io in the circuit using mesh analysis

Applying KVL to mesh 1,

(8+j10-j2)I1-(-j2)I2-j10I3=0

Mesh 2,

(4-j2-j2)I2-(-j2)I1-(-j2)I3+20angle90=0

Mesh 3, I3=5 We must substitue this in equation 1 and 2,

(8+j8)I1+j2I2=j50

j2I1+(4-j4)I2=-j20-j10

Put it in matrix form as

   | 8+j8            j2  |     I1=|j50|

         |         j2         4-j4|  I2=|-j30 |

from wiche we obtain the derminants

delta=68

delta 2=416.17angle -35.22

where I2=Delta2/delta=416.17angle-35.22/68

I2=6.12angle-35.22 A      

Supermesh

-supermesh analysis is a better technique instead of using mesh analyis such a complex electric circuit where two meshes have a current source as a common element. This is the same with supernode analysis which we also use when voltage source has a common node in the circuit.