This is basic Mathematics from introductory Differential Calculus. Refresh your memory from any Calculus book; if you don't know Calculus at all read Calculus: Basic Concepts for High Schools by Tarasov which you can get here - https://mirtitles.org/2018/09/04/calculus-basic-concepts-for...
Your picture is simple enough; but you have mixed up dq (this is the dependent function on the Y-axis) and dt (this is the independent variable on the X-axis) infinitesimals. Their ratio is simply the instantaneous rate of change of electric charge w.r.t. time which is what is the instantaneous electric current. As to the cross-sectional area of a wire varying over its length and how it affects current through it, you can neglect it for short wires and using a specific wire gauge for all normal electronics.
> There needs to be an even more grounded book in electronics, something that you can show to a guy who literally has no idea about electronics in the slightest bit and by the end of the book, the guy is a master at it
Electronics = Physics+Mathematics+Logical Thinking and there can be no shortcuts to its study. You have to put in some effort to study the subject. However things have been simplified and modularized to such a great extent nowadays that you can learn and do a great deal without understanding much of the mathematics and physics involved. The submitted book link in this post is a good basic one to start from.
I would love a book that gives a layman’s understanding of how to read and dissect a board you pull out of common modern device.
Say a roomba.
You might not know how or why each component works in detail at the end, but instead understand why the board is laid out the way it is and where each component controlling the functions and logic live, what might be broken, and whether and how to repair. I think if I were an impatient student with an interest in electronics that’s what I’d want. Then go back and study individual components, math, physics, and theory.
You could make a whole series: radio boards, home appliance boards, PC motherboards, car boards, etc.
Reverse Engineering a PCB is a well known field (https://en.wikipedia.org/wiki/PCB_reverse_engineering); but you still have to have some knowledge of individual components, math, physics, and theory before you can get started with this.
There is plenty of material and videos on the web if you search for it; also a book The Art of PCB Reverse Engineering: Unraveling the Beauty of the Original Design by Ng Keng Tiong.
Your picture is simple enough; but you have mixed up dq (this is the dependent function on the Y-axis) and dt (this is the independent variable on the X-axis) infinitesimals. Their ratio is simply the instantaneous rate of change of electric charge w.r.t. time which is what is the instantaneous electric current. As to the cross-sectional area of a wire varying over its length and how it affects current through it, you can neglect it for short wires and using a specific wire gauge for all normal electronics.
> There needs to be an even more grounded book in electronics, something that you can show to a guy who literally has no idea about electronics in the slightest bit and by the end of the book, the guy is a master at it
Electronics = Physics+Mathematics+Logical Thinking and there can be no shortcuts to its study. You have to put in some effort to study the subject. However things have been simplified and modularized to such a great extent nowadays that you can learn and do a great deal without understanding much of the mathematics and physics involved. The submitted book link in this post is a good basic one to start from.