Analysis Methods

THE MESH CURRENT METHOD

In the mesh current method a current is assigned to each window of the network such that thecurrents complete a closed loop. They are sometimes referred to as loop currents. Each element andbranch therefore will have an independent current. When a branch has two of the mesh currents, theactual current is given by their algebraic sum. The assigned mesh currents may have either clockwise or counterclockwise directions, although at the outset it is wise to assign to all of the mesh currents aclockwise direction. Once the currents are assigned, Kirchhoff’s voltage law is written for each loop toobtain the necessary simultaneous equations

EXAMPLE

Obtain the current in each branch of the network shown in Fig.  using the mesh current method

                                                                        

 

The currents I1 and I2 are chosen as shown on the circuit diagramApplying KVL around the left loopstarting at point

 

-20 + 5I 1+10( I1-I2 ) = 0

8+10( I2 –I1 ) + 2I2         = 0

15I1 -10I2  = 20

-10I1 +12I2 = –8

 

I1 = 2A and I2 = 1 A. The current in the center branch, shown dotted is I1 - I2 = 1 A