For a circuit like this:

1. What kind of methods can I use to find equivalent voltage source for the 7A current source beside using supermesh current analysis?


2. Also, when using supermesh current analysis, we first remove the current source and form a supermesh current. Why do we do that? And what's the logic behind such move?

Thank.

 

The three highly formalized analysis techniques are MCA (Mesh Current Analysis), NVA (Node Voltage Analysis), and Superposition. Beyond that you have the more fundamental but less formal ad hoc approaches using combinations of KVL and KCL, often involving combining resistances (or impedances to be more general) as much as possible. This may involve reducing the circuit to a very simple circuit that lets you determine the overall current, but not the voltage or current you are interested in. But, with that found, you can now start expanding the circuit back out incrementally finding additional voltages and currents along the way until you get to the ones you are interested it. The ad hoc methods can involve a bit of art and cleverness, whereas the formalized methods are recipes that are guaranteed to work (on circuits that are solvable at all) even if applied blindly.

This particular problem, for me, screams out for the use of NVA at first glance -- you have three nodes (not counting the bottom node, which is the ideal choice for 0V) but one of them you know immediately is 7V. I generally shy away from MCA if there is an interior current source (i.e., one that is shared by two meshes). If the current sources are on the exterior branches (i.e., only involved in one mesh), then they make MCA easier to use.

In this case, notice that the 7V source can simply be moved to the right side of the circuit without changing a thing, placing the current source in an exterior branch. Doing that makes MCA very straight forward. You have three meshes, but one of them is directly solvable as being 7A.

But let's say that we couldn't move the current source to an exterior branch and wanted to use mesh analysis. Remember that MCA is nothing more than a very formalized application of KVL and, therefore, we need to be able to write the voltage drops for each component around the mesh as we get to it, either directly (in the case of a voltage source) or in terms of the mesh currents (times a resistance/impedance of that component). [Let's not complicate the discussion with dependent sources, but the same idea applies there, as well.] Each mesh will produce one equation.

But we can't do this for a current source because the voltage across it is not a direct function of the mesh currents and the strenth of the source, but rather an interaction of the strength of the source and all of the components. But what it does do is impose a very easy to describe relationship between two mesh currents. So we take the two adjacent meshes as a pair and develop a pair of equations from them. We note the relationship between the two mesh currents that is imposed by the current source in the shared branch as one of our mesh equations. We then write down the equation for the supermesh (the two meshes combined) by jumping from one mesh to the other when we encounter the branch. We use the exact same idea to write down the mesh equation for the supermesh as we would for a normal mesh.

This has a directly analogous situation in NVA when you have a voltage source in a branch. Because the current in the voltage source is determined by an interaction of the source and all the nodes, we use the source to establish a relationship between two nodes and then apply KCL to the two-node 'supernode' using the same concept that we use when dealing with a single node.