In fact, this method gets its name from the idea of these currents meshing together between loops like sets of spinning gears: The strangest part of the Mesh Current method is envisioning circulating currents in each of the loops. In our example circuit, the loop formed by B 1, R 1, and R 2 will be the first while the loop formed by B 2, R 2, and R 3 will be the second. The first step in the Mesh Current method is to identify “loops” within the circuit encompassing all components. Let’s see how this method works on the same example problem: It differs from the Branch Current method in that it does not use Kirchhoff’s Current Law (KCL), and it is usually able to solve a circuit with less unknown variables and less simultaneous equations, which is especially nice if you’re forced to solve without a calculator. The Mesh-Current Method, also known as the Loop Current Method, is quite similar to the Branch Current method in that it uses simultaneous equations, Kirchhoff’s Voltage Law (KVL), and Ohm’s Law to determine unknown currents in a network.
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