This paper presents a new state-space approach for temporal analysis of electrical circuits. The method systematically obtains the state-space formulation of nondegenerate linear networks without using concepts of topology. It employs nodal/mesh systematic analysis to reduce the number of undesired variables. This approach helps students to understand how a circuit works with energy-storage elements. In addition, students perceive the method to be an extension of the analysis of static networks, integrating the new concepts in an unified framework. The assessment results show that significantly more of the students who achieve higher scores in circuit analysis have learned the state-space approach rather than the conventional methods. (Contains 5 figures.)