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!

 

Hello there
welcome to AAC
Make yourself at home pull up a chair ,relax this place has everything come on I'll show you.
https://forum.allaboutcircuits.com/threads/supermesh-and-supernode.55197/

Thanks for your answer and the help! There was some usefull articles in that link.
According to what i have read i think the KVL i performed was correct. I enclosed the voltage source between node 1 and 3 (no paralllel element connected with that voltage source in my case) and i accualy add up the voltage drops in the series circuit created by the loop i named B in the circuit above. (what KVL accualy is according to the link's information). I hope i get it right.
Thanks for your help again.

 

According to what i have read i think the KVL i performed was correct.

If you are doing nodal analysis with supernodes, then KVL has no place in the solution. Nodal analysis applies KCL to obtain the node equations, but the currents are expressed in terms of the node voltages & any dependent sources must be expressed in terms of the node voltages. Also, if there is a reference/ground node then that needs to be identified on the circuit diagram.