Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

example: 4.8-2
Find the total power dissipated in the circuit and power delivered by each source in Fig. 4.8-3.
V
3
V
1
–11 V
4 V
5 V
1 A
2 A
2 
Ω
3 
Ω
4 
Ω
1 
Ω
1 
Ω
+
+
+
+
–
–
–
+
–
+
+
+
–
–
–
–
V
2
R
1
R
2
R
3
R
4
R
5
i
1
I
1
I
2
Fig. 4.8-3 
Circuit for Example 4.8-2 
Solution
There is no current source that can be transformed into a voltage source in this circuit. However, the 
current source I
1
directly constrains the second mesh current to be 2A. The third mesh current gets 
constrained to be I
1
+
I
2
=
3A. Therefore, there is no need to assign mesh current variables in second 
and third meshes. The mesh current variable i
1
is assigned to first mesh as shown in Fig. 4.8-3.
The mesh equation for the first mesh is 5i
1
=
4V
+ 
3
W × 
2A
- 
5V 
=
5V 
×
i
1
=
1A. The complete 
solution is shown in Fig. 4.8-4.
V
3
V
1
–11 V
4 V
–1 A
–1 A
5 V
3 V
2 V
–2 V
2 V
1 V
12 V
–1 V
1 A
1 A
1 A
1 A
3 A
3 A
2 A
2 A
+
+
+
+
+
–
–
–
–
+
–
+
+
+
+
–
–
–
–
–
V
2
I
2
I
1
1A
2A
3A
Fig. 4.8-4 
Circuit solution for Example 4.8-2 
We have followed passive sign convention throughout. Hence, the power dissipated in each resistor 
is the product of voltage across it and current through it. Total power dissipated in the circuit is found 
by adding up this product for all the resistors.

---

Mesh Analysis of Circuits with Independent Current Sources 
4.37
\
Total power dissipated in the circuit 
=
2V 
× 
1A 
+
3V 
× 
1A 
+
2V 
× 
2A 
+
1V 
× 
1A 
+
12V 
× 
3A 
=
46 W
Power delivered by an element is equal to negative of power dissipated in it. Power dissipated in 
an element is the product of voltage and current as per passive sign convention. Hence, the power 
delivered by a source is negative of vi product with v and i marked according to passive sign convention.
\
Power delivered by V
1
=
-
(4V 
×
-
1A) 
=
4 W
Power delivered by V
2
=
-
(5V 
×
-
1A) 
=
5 W
Power delivered by V
3
=
-
(
-
11V 
×
3A) 
=
33 W
Power delivered by I
1
=
-
(
-
1V 
×
2A) 
=
2 W
Power delivered by I
2
=
-
(
-
2V 
×
1A) 
=
2 W
The total delivered power is equal to the total dissipated power.
The last two examples have demonstrated that:
a) An independent current source imposes a constraint on mesh current variables and reduces their 
number by one.
b) A mesh current variable need not be assigned for a mesh if an independent current source 
determines that mesh current directly or indirectly through another mesh variable assigned to 
another mesh.
c) Mesh equation for a mesh in which the mesh current is fixed directly by an independent current 
source appearing only in that is not required for solving other mesh current variables.
d) Mesh equations for two meshes that share an independent current source among them have to 
be added to get a combined mesh equation that will be useful in solving the circuit analysis 
problem.
e) The mesh analysis formulation results in an equation