Voltage maps simplify electric circuit analysis

Abstract

The pioneering work over 50 years ago by M.I.T. faculty who wrote textbooks for the study of electrical sciences set the pattern for the study of electric circuits in the United States. Authors who developed textbooks after those early works largely followed the techniques advanced there. This paper extends the analytical procedures adopted for identifying current direction and voltage polarities in a circuit. While the M.I.T. works adopted an arrow to indicate current direction, a similar arrow symbol for voltage was not adopted. Double subscript notation identifying nodes and relative polarity was used instead. This notation has contributed to confusion of students who are learning electric circuits. A simpler designation of voltage polarity by an open-head arrow promotes a better understanding of electric circuit operation. This paper proposes the use of a closed-head arrow for current direction, and an open-head arrow for a voltage rise between nodes. In this method all voltages are rises only. All voltages can be drawn in a voltage map of a circuit, using open-head arrows to show both voltage rises from sources of emf and voltage rises across resistors caused by Ohm's law relationships. This proposed method for identifying voltages corresponds with the node voltage polarity terminology used to interpret results from computer software programs such as PSPICE. A consistent conformity with symbols in circuit analysis is an enhancement to learning for the beginning student of electric circuit analysis. The voltage map is such a learning enhancement.<>