Introduction to Electric Circuits

7.4 Mesh current analysis 161

For mesh 2

1 The coefficient of the mesh current is the sum of the resistances around the
mesh (=R2 + R3 + R4). We therefore have (R2 + R3 + R4)I2 on the left-
hand side of the equation.

2 There are two adjacent meshes (1 and 3). The resistance common to meshes
2 and 1 is R2 and the resistance common to meshes 2 and 3 is R4. We
therefore have terms -Rfl~ and -R4I 3 on the left-hand side.

3 There is a voltage source Vs2 acting in the same direction as the mesh
current so § Vs2 appears on the right-hand side of the equation.

The mesh equation is therefore

-R2I 1 + (R 2 + R 3 + R3)I 2 -- R4~- Ys2 (7.20)

For mesh 3

1 The total resistance around the mesh is (R4 + Rs) so we have (R4 + R5)I3 on

the left-hand side of the equation.

2 There is one adjacent mesh (2) and the resistance common to it and mesh 3
is R4. We therefore have a term -R412 appearing on the left-hand side.

3 The voltage source Vs3 acts in the opposite direction to the mesh current so
that -Vs3 appears on the right-hand side.

The mesh equation is therefore

-R412 + (R4 + R5)I3 = -Vs3

In matrix form the equations may be written

IR+R2, RE 0 I I,l rvs1
-R 2 (8 2 + R 3 -Jr- R4) -R 4 12 - /Vs2 [

• R4 (R, + 6 L-

(7.21)

(7.22)

Example 7.14

Determine the currents supplied by the voltage sources Vs1 and Vs2 in the

circuit of Fig. 7.11.

Figure 7.11

R1 - 49~ R3 = 3D. R5 = 5s

......................... i 1