I'm studying these three methods and i'm confused on exactly which one is used when. This is a very broad question. Therefore, could some explain in general terms the difference of the three methods as this might bring some clarification to me instead.
As I'm understanding Mesh analysis is KVL and Node analysis is KCL? Am I right here or wrong? Where does superposition come from?
KVL states that the sum of voltages around a circuit (loop) is zero. Multiple interconnected loops create a mesh. This allows you to write down a system of equations that can be solved for all of the voltages (and currents) in the mesh. So yes, KVL and mesh analysis are closely related.
Similarly, KCL states that the sum of currents into (or out of) a node is zero. This allows you to write down a different system of equations that can be solve for all of the currents (and voltages) in the circuit (collection of interconnected nodes). KCL and nodal analysis are closely related.
Superposition is an approach used to deal with linear circuits that have multiple indpendence sources, in which you evaluate each independent source, one at a time, and then add the results together. Mesh or nodal analysis might be used for the individual solutions.
Node Voltage analysis and Mesh Current analysis are circuit analysis techniques that apply KCL and KVL systematically. In Node Voltage analysis, you apply KCL at each unknown node in the circuit (i.e. sum the currents flowing out of the node). In Mesh Current analysis, you apply KVL around each mesh in the circuit.
The heart of you question is a common one: what technique should I apply to analyze the circuit? In general, there are many approaches to circuit analysis, and it is a matter of preference when choosing between different methods; fortunately, the choice between Node Voltage analysis and Mesh Current analysis is unambiguous. Both methods reduce to solving a system of linear equations (i.e. n equations and n unknowns). To choose between methods, pick the one that involves solving the fewest equations. For example, if a circuit has 3 nodes and 3 meshes, Node Voltage analysis involves solving 3-1=2 equations (we define one of the nodes to be zero volts); on the other hand, Mesh Current analysis requires solving 3 equations.
The linear systems generated by Node Voltage and Mesh Current analysis methods can be put in matrix form: $$Ax=b,$$ which can be solved by $$x=A^{-1}b$$ when the matrix A is non-singular (which is true for reasonable circuits).
Superposition as a circuit analysis tool takes advantage of the linear nature of these circuits, allowing specific currents and voltages to be solved for by deactivating all but one independent source at a time. In this way, is related to the discussion above (solutions could be put in matrix form, but this is not typically necessary). While the principle of superposition is useful, it is less structured (read algorithmic) than Node/Mesh analysis.
The number of equations should be the main concern in the selection of the analysis method. but if the number of equations comes out to be the same then look at the required value if currents are required then prefer mesh if voltages are to be calculated then choose nodal it will give you direct result
