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In response to demands from industry and the profession for more graduates, first-year engineering numbers have grown considerably over the last decade, matched by an increasing diversity of academic backgrounds. In order to support first-year students effectively, and ensure the courses they take remain appropriately pitched, the academic preparedness of these students must be determined. Since 2007, the lecturers in the compulsory first-year Electrical and Digital Systems course at the University of Auckland (UoA), Auckland, New Zealand, have administered a short diagnostic test to determine the level of conceptual understanding of electricity and electromagnetics possessed by the incoming students. This paper presents and discusses student understanding of dc circuit theory as revealed by the diagnostic test and subsequent investigations. The evidence is indicative of both flawed conceptual models and context-triggered misapplication of fundamental rules. Parallels are drawn with the results of research conducted elsewhere, indicating the misconceptions are robust and pervasive, crossing institutional and national boundaries. Not only are concepts such as current and voltage poorly understood, but even more basic concepts such as series and parallel connections are confusing for a significant number of students. Understanding the incorrect models that underlie these basic misconceptions is the first step to correcting them. Only then can students proceed to the more advanced concepts that engineering graduates are required to master.