Applications of Linear Algebra to Electrical Engineering Research Paper

Applications of Linear Algebra to Electrical Engineering - Research Paper Example This paper illustrates that matrices are used to find the simplest method of solving complex electrical circuits. A mesh is a loop that has a single current flow path. In the circuits where there are different current paths and different voltages, the simplest method is to utilize the matrices to solve for the currents and voltages. Every electrical network must have three basic quantities current, voltage or potential difference and resistance. There could be impedance or reactance at the place of resistance but the two quantities voltages and current are the constant in every electrical network. Many scientists proposed theories shoe the relation between the voltage or potential difference, current and resistance but ohms law presented the best relation in between the three quantities. The writers ‘Shamieh Cathleen and Gordon McComb’ in the book ‘Electronic for Dummies’ write â€Å"Ohm’s law is a master key, unlocking the secrets to the electronic circuits†. The problem then arose in solving the complex electrical networks, which have more than one resistance, current, and voltages. At every loop, the current is different and at every node, the difference in voltage and current could be seen. To solve the matter the engineers and scientists relied upon utilizing the different mathematical methods and formulas but linear algebra has the right method to solve the complex electrical circuits and electrical networks. Kirchhoff’s laws presented by Gustav Kirchhoff in 1845 relate to the power conservation in the electrical circuits and have vast applications in electrical engineering. As we know the Ohm’s law states that V = IR, it is the simplest estimation to calculate the voltage or current into the circuit if the third variable is known. Kirchhoff’s voltage law states, â€Å"The algebraic sum of the voltages around any closed path in a circuit is identically zero for all time†. In this way, if we consider a mesh in which, there only a single loop, the method that represents the mesh current is used to the determine the current in each of the mesh. If we have a single loop consider the situation, it will be easier to evaluate the unknown quantity but it the circuit consists of several mesh circuits, the will be complex to evaluate an unknown current in different mesh circuits. For this reason, Kirchhoff’s voltage law provided an easier method to apply it to every mesh of the circuit. It should be kept in mind the circuit contains resistances, and if a mesh has a resistor that the other mesh also has, the voltage must be the product of the resistance and the subtraction of analyzed current and other currents.