Circuit theory is one of the most important tools of the electrical engineer, and it can be derived with suitable approximations from Maxwell's equations. Despite this, university courses treat electromagnetism and circuit theory as two separate subjects and at advanced level, students can lack a basic understanding of the classical electromagnetism applied in the context of electric circuits to fully appreciate and apply circuit theory and understand its limitations. Here the authors build on their graduate teaching experiences and lectures to treat these topics as a single subject and derive and present the important results from circuit analyses, such as Kirchhoff's laws and Ohm's law, using the ideas of the classical electromagnetism.