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Mesh Current Method

What the Heck is the Mesh Current?
Let's discuss about the identity of mesh current first. What the heck is this illusive, non-physical current? The tem “current” we use is the current through an element, or “element current.” On the other hand, mesh current is defined as the current that exists only in the perimeter of a mesh. In a simple single loop circuit (a circuit for example with a voltage source connected sequentially to two resistors in series), the term “current only in the perimeter” is not confusing at all.  The mesh current along the only mesh  is the same as the element currents (the current flowing through the source or the resistors).

Mesh Current vs. Element Current
In a circuit with more than 1 meshes, the term mesh current is slightly confusing.   Especially two meshes meet together at a branch than two different mesh currents assume to flow in the same branch!  In a branch, how can we have two mesh currents?   The answer is the mesh current is the invention of convenience.  Think about this way.  In an element or branch where two meshes meet together, any current (element or branch.  Actually two are the same) can be taken as a net current of two imaginary currents flowing through the branch.

Cash Flow again
Cash Flow is a good analogy for the branch current.  Then, your income and expense are two mesh current.  The cash flow of your household or your account is determined by income minus expense.  When you check your monthly balance, you see only the cash flow: how much gain or loss do you see in the sheet.  Not each income of expense.

KVL in Disguise
We can say this statement, then, that mesh current method is actually applying KVL around a mesh with “net voltage drop” across an element.

Order of KVL Application
Here is the order of mesh current method application:
a. Assign mesh currents to the meshes
b. Using Ohm’s Law, express the voltages in a mesh in terms of the mesh current
c. Apply KVL to each mesh
d. Solve the resulting simultaneous equation to get the mesh current

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