# Nodal analysis with supernodes

#### miltoskotoulas

Joined Nov 22, 2020
2
Hello everyone and sorry for my bad english.
I had a homework on analysing circuits using nodal analysis with supernodes(one or more voltage sources connected to two non refference nodes). Althought i had complete the homework i kept exercising on circuits until i found that one:

I know that there are two super nodes in that circuit (node 1 and 2 forms a supernode and node 1 and 3 forms another supernode). So firstly i am taking KCL in both supernodes.

KCL in supernode 1,2 : i1+i2+i3=0 ⇒ v1/4 + v2/1 + (v3-v2)/2 =0 (1)
KCL in supernode 1,3 : i1 + i = i3 ⇒ v1/4 + v3/4=(v2-v3)/4 (2)

Now according to theory i must take KVL to solve the system. Althought i can take KVL in loop A which contains the voltage source of 2i V i want to take just for shake of better understanding the loop B that contains the 2i V and the 12 V voltage sources since i can do that also according to theory.
What i am doing is:
KVL in the mesh B : -2i+12 -2i3=0 ⇒-2(v3/4)+12 -2((v3-v2)/2)=0 (3)

Is the last equation correct?

Is there a better and easier way to perfom KVL in supernodes?
Thank you!

#### miltoskotoulas

Joined Nov 22, 2020
2
Hello there
welcome to AAC
Make yourself at home pull up a chair ,relax this place has everything come on I'll show you.