Use of linear algebra in electrical circuit engineering

To begin with we shall present Kirchhoff’s Laws. Kirchhoff’s Current Law (First Law): The algebraic sum of all currents at any branch point is zero. Kirchhoff’s Voltage Law (Second Law): The algebraic sum of all voltage changes around a loop is zero. Electrical engineers use Kirchoff`s current law and Kirchoff`s voltage law to write a system of linear equations. This procedure is going to be described below.

1) It is necessary to draw the circuit and assign labels to the unknown quantities, including currents in each branch.

Also it is necessary to assign directions to currents. The answer resulting from the analysis will come out positive if the direction of a particular unknown current is guessed correctly and come out negative otherwise. In both cases the magnitude of the current will be right. 2) Then the Kirchhoff’s Current Law is applied to as many junctions in the circuit as possible to obtain all independent relations.

3) As the next step the Kirchhoff’s Voltage Law is applied to as many loops in the circuit as necessary in order to solve for the unknowns.

If one has n unknowns in a circuit one will need n independent equations. In general there will be more loops present in a circuit than one needs to solve for all the unknowns. 4) And finally it is necessary to solve the resulting set of simultaneous equations for the unknown quantities. The simplest solution for this set of equations is executed within the linear algebra methods.