# How to use a supernode or supermesh with regard to this circuit?

Is the two ohm resistor in parallel with the dependent current source disregarded when using a supermesh? I have not gotten the correct answer of Va=1V Vx=-4 . What are the steps?

• The are five 2 Ohm resistors and none of them is in parallel to any other component. Which one do you mean when you talk about the 2 Ohm resistor? – Curd Sep 25 '17 at 17:19

Supernodes are used to do nodal analysis on circuits containing voltage sources. You would make a supernode from each pair of nodes that are connected by a voltage source.

Since you ask specifically about the supermesh, I won't give any more detail about supernodes. If you want more detail, you need to name all the nodes in your circuit.

Supermeshes are used to do mesh analysis on circuits containing current sources. You make a supermesh for each pair of meshes where a current source lies on a branch shared by two meshes.

For example, in your circuit, let's call the left mesh (containing the 5 V source) #1, the upper right mesh (containing the $2 I_x$ CCVS) #2, and the lower right mesh (containing the 7 V source) #3. We'll define all mesh currents in the clockwise direction.

Now mesh currents $I_2$ and $I_3$ can't be determined independently because of the VCCS $0.8 V_x$.

So you create a supermesh $I_{23}$ encompassing those two meshes, with a joining equation $I_2 - 0.8 V_x - I_3 = 0$. The mesh equation for the supermesh is made by following the outer perimeter of the supermesh and algebraically summing the voltage drops:

$$-9\mathrm{V} - 2 I_x + 2 I_3 - 7 \mathrm{V} - 2 I_3 - 2 (I_3 - I_1) = 0$$

• @anonymous editor: You are trying to edit the last equation to use a different sign convention than I used when writing it. Your version would be correct if the mesh current was taken counter clockwise rather than clockwise. But since I said I will take the current clockwise, this change is incorrect. Please stop editing. – The Photon Mar 20 '18 at 21:09