Introduction to Electric Circuits

7.4 Mesh current analysis 167

The supermesh equation is therefore

RlI 1 + R212 - R213 = _Vsl

Now I 1 -- I 2 = Is ~ 11 = Is + 12, so

Rl(Is + 12) + R212- R213 = -Vs,

Putting in the values,

6(5 + 12) + 312- 313 = -12
912- 313 = -42

Dividing through by 3 we get

312- 13 = -14 (7.32)

For mesh 3:

1 we multiply the mesh current by the resistance through which it flows

(R 2 + R3);

2 there is one adjacent mesh whose current (I2) is multiplied by the resistance
common to both meshes (R2);

3 the voltage source Vs2 acts in the opposite direction to the current in the
mesh so the right-hand side of the mesh equation is -Vs2.

The mesh equation is therefore

(R2 + R3)I3- R212 = -Vs2

Putting in the numbers and rearranging we have

-312 + 1813 = -3 (7.33)

Adding Equations (7.32) and (7.33) we have

1713=-17 and 13=-1A

The minus sign indicates that the mesh current 13 flows in the opposite direction

to that shown in the diagram (i.e. anticlockwise rather than clockwise).

(1) To find the mesh current 12

Substituting for 13 =-1 A in Equation (7.32) we have 312- (-1)=-14

and

12 = -15/3 = -5 A

Again the minus sign indicates that the mesh current 12 flows in an anticlock-

wise direction around the mesh.

(2) To find the voltage at node X

The voltage at node X is given by

Vx = Vs2 + 13R3 = 3 + (-1) • 15 = 3- 15 = -12V