Application of Gaussian in circuit theory, using Kirchhoff�s 2nd law. In this paper for a given circuit, forming into matrices form by using Kirchhoff�s 2nd law we solve and find the current values. Less than 3x3 matrices we can use Carmel�s rule, but more that 3x3, Carmel�s cannot be done, so gauss elimination method is used to find the current values for the given circuits