Graph theoreticanalysis of an electrical circuit with unknown resistances and voltages

Electrical circuits can be studied and simplified by using many well known theorems of Electrical Engineering. An electrical circuit can be represented by graph also. The circuit diagram can be converted to different matrices by using specific definitions. There are many matrix equilibrium equations which can be obtained from different laws of electrical circuits. The results of these equations can be verified by the existing theorems and graph theory. Some difficult problems become interesting and also look simple when represented using a graph. Graph theory is useful and powerful technique for solving real-world problems as it gives different kinds of optimization. It seems to be laborious to use the existing and traditional methods to find branch currents and loop currents of electrical circuits if it contains many branches. Using mathematical model this difficulty can be solved. In our previous paper we analysed currents in a circuit with all known resistances and voltages. In this paper, branch currents of an electrical circuit with unknown resistances and voltage are obtained using network equilibrium equations and then it will be verified by Thevenin’s theorem.