Taming the Load Current of Identical Cells in Matrix

Abstract

We explore the load current [Formula: see text] for a rectangular array (matrix) of [Formula: see text] identical cells where [Formula: see text] strings (columns) of [Formula: see text] serial cells (rows) are arrayed in parallel. [Formula: see text] is equal to [Formula: see text] with the internal resistance of the cell and the load resistance exchanged. By treating a linear fractional function as a translated inversely-proportional function, we can easily capture the properties of [Formula: see text] and the relative magnitude of [Formula: see text] and [Formula: see text] via their ratio. The limiting behaviors of the load current are discussed beyond the ideal-cell and short-circuit limits. For the given total number of cells, we graphically verify the recent findings on the matrix of cells that produces the maximum load current. Finally, we analyze the possibility of a car starting with lemon cells or AA dry cells in matrix. This work would be useful in creating a high school or university curriculum that unifies identical cells in series, parallel, or matrix.