Modified Impedance Matching in a Discrete Battery System: Selection Rule for Maximum Power Transfer

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.Beyond the maximum power transfer theorem, we suggest a class of linear two-terminal circuits where impedance matching is the condition for maximum power transfer to a fixed load resistor. As such a discrete case, for a given total number of identical cells, impedance matching has been used to find the maximum load current (MLC) (hence, maximum load power) when all possible series-parallel combinations (SPCs) of cells are connected to a load resistor. When the impedance matching solution is located between two adjacent SPCs in the ordered list of SPCs, a simple selection rule for determining which of the two combinations gives the MLC without directly calculating and comparing their load currents is presented in this article. As a by-product, the spectrum of SPCs producing the MLC for a given total number of cells can be obtained as a function of the resistance ratio (internal resistance of the cell/load resistance).