Problem 1-10: Solving by Nodal Analysis – Circuit with Four Nodes

Solve the circuit by nodal analysis and find .


Solution
a) Choose a reference node, label node voltages:


b) Apply KCL to each node:

Node 1:
(1)

Node 2:
(2)

Node 3:
(3)
(1), (2) and (3) imply that and .

c) Find the required quantities:

If we apply KVL in the loop shown above:

.