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2.5 
analysIs of a sIngle-node-paIr cIrcuIt
A set of circuit elements is said to be connected in parallel if they have two nodes in common. 
Fig. 2.5-1 shows three circuit elements connected in parallel. All the three elements have one of 
their terminals connected at node-A and the other terminal connected at node-B. Circuit in Fig. 2.5-
1(a) shows reference polarity assignment for the element voltage variables for the three elements. 
The terminal connected to the node-A is assigned the positive polarity in all the elements in this 
case. Circuit in Fig. 2.5-1(b) shows another possible polarity assignment. Here, the terminal that is 
connected to node-B is assigned the positive polarity of voltage variable in the case of second element.
(a)
v
1
v
2
v
3
A
B
+
+
+
–
–
–
(b)
v
1
v
2
v
3
A
B
+
–
+
+
–
–
Fig. 2.5-1 
Parallel connection of elements
This circuit has two meshes. We can apply KVL in those meshes. KVL applied to meshes in circuit 
in Fig. 2.5-1(a) will show that v
1
=
v
2
=
v
3
in the circuit. However, KVL applied to meshes in circuit 
in Fig. 2.5-1(b) will show that v
1
=
-
v
2
=
v
3
. Thus, the terminal voltages of elements connected in 
parallel will have same value at all t if same reference polarity assignment is used for all of them. That 
is, parallel-connected elements have a common terminal voltage if reference polarity is same for all 
of them. Therefore, it is a standard practice in circuit analysis to assign positive polarity to terminals 
connected to a common node in the case of a set of parallel-connected elements.
A set of parallel-connected elements result in one node-pair. There will only be one independent 
KCL equation in a circuit containing just one node-pair. However, such a circuit may contain many 
meshes. Applying KVL in all those meshes will result in an already-noted conclusion that all the 
elements in parallel will have same terminal voltage.