I worked my way through the paper you recommended. Probably a first for me to bother with the mathematics surrounding a transistor. I award myself a Vc (Victoria cross) that I did it and survived. I had to look up what KVL means and am quite pleased with myself that I was able to work out V(RE) for myself in 4.7.2
But I know that I have missed the point the paper was trying to convey. For instance in 4.7.1 the LED and resistor are together, and in 4.7.2 they are on either side of the transistor. Is this important at all?
In 4.7.1 there is a base resistor, and 4.7.2 there is none. Is there some point to that?
As a personality flaw, I despise details, which probably explains why I hate maths. I just need someone to tell me, does it matter when placing a motor and transistor together in series whether the motor is on top (common emitter) or on the bottom (common collector). I will take their word for it (without mathematical proof) if they say yes it matters, one generally places a motor in common collector mode.
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The following is what shako.ai said in answer to my question "which is a better way to connect a transistor and motor in series, common emitter or common collector mode?". "In general, common emitter mode is better for driving low-current loads, such as LEDs or sensors, while common collector mode is better for driving high-current loads, such as motors or speakers."
Yet when I do a Google search for "dc motor and transistor circuit" almost every circuit has the motor in common emitter mode.
Thanks again, it was a new experience for me.