Introduction to Electric Circuits

160 Nodal and mesh analysis

the three mesh currents or Cramer's rule can be used to solve the matrix
equation (7.18).
We note from Equations (7.15), (7.16) and (7.17) that to form a particular
mesh equation we:

1 multiply that mesh current by the sum of all the resistances around that

mesh;

2 subtract the product of each adjacent mesh current and the resistance
common to both meshes;

3 equate this to the voltage in the mesh, the sign being positive if the voltage
source acts in the same direction as the mesh current and negative
otherwise.

Example 7.13

For the circuit of Fig. 7.10 write down the three mesh equations from which the
mesh currents 11, 12 and 13 could be determined.

Figure 7.10

R1 R3 R5

i iii r--q l I

@

t

0

Vs2

Vs3

Solution

To set up the mesh equations we follow the three steps outlined above.

For mesh 1

1 The coefficient of I1 is the sum of the resistances around the mesh

(=R~ + R2). We therefore have (R~ + R2)ll on the left-hand side of the

equation.

2 There is one adjacent mesh whose current is I2. The coefficient of I2 is

minus the resistance common to meshes 1 and 2 (i.e. -R2). We thus have

-R212 on the left-hand side.

3 The right-hand side of the equation is Vs~, positive, as the source acts in the

same direction as the mesh current.

The mesh equation is therefore

(R1 + R2)I1- R212 = Vsl (7.19)