Use node analysis to find the node voltages e1 and e2 in the

Use node analysis to find the node voltages e_1 and e_2 in the circuit below.

Solution

Applying nodal analysis

At node 1

[(e1-e2) / 4] + (e1 / 2) = 5

3e1 - e2 = 20 ------1

At Node 2

[ (e2 - e1) / 4 ] + (e2 / 6) +5 = 10

(e1 / 4) - (5 e1/ 12) = -5 -----\'-2

By solving 1 and 2 we get

e1 =13.34 v

e2 =20.04 v