2026 ASEE Annual Conference & Exposition

In both associate and baccalaureate engineering technology programs, most students take the first electric circuits course before taking a calculus course. Therefore, the first circuit analysis course typically avoids the use of calculus, instead using only algebra and trigonometry. One such example is the derivation and use of the maximum power transfer theorem for dc and ac circuits.

This paper will present a detailed algebra-based derivation of the maximum power transfer theorem for dc circuits using the calculus-free arithmetic mean-geometric mean (AM-GM) inequality. The AM-GM inequality will be presented graphically as well. For ac circuits, the paper will present detailed algebra-based derivations of the maximum average power transfer theorem for four types of loads: variable resistive element and variable reactive element, variable resistive element and fixed reactive element, fixed resistive element and variable reactive element, and variable resistive element with no reactive element. All of the derivations will purposefully avoid the use of calculus; however, the resulting equations will match exactly with the ones typically derived using calculus in introductory circuits textbooks.

Additionally, in support of broadening the pedagogical perspectives, verification of the algebra-based derived equations and proven theorems will be presented using LTspice simulation. It is to be noted that LTspice is a powerful yet freely downloadable circuit simulation software, and can be used effectively to add a graphical perspective to the understanding of key circuit equations and theorems.

The full paper will provide complete algebra-based derivations of the maximum power transfer theorem for dc and ac circuits, including multiple resistive and reactive load element combinations for ac circuits. All derived equations and results will be supported by graphical verification using a circuit simulation software. The work to be included in the proposed paper will aid the instructors in presenting the maximum power transfer theorem for electric circuits in a non-calculus approach to the entry level engineering technology students.