NPN calculations

In an attempt to keep these calculations organized, here's the maths for NPNs.

(From: https://www.youtube.com/watch?v=ZEDdFjvnAAo)
Suppose you had a 5v/2A source and wanted to power a 5v 1A motor via mCu board (which can only source 5v/0.5A). What would the resistor need to be on the Base of the NPN?

If you have a hRE 100 NPN transistor here's the formula:

Ic = Collector current
Ib = Base current

Solving for Ib
hFE = Ic / Ib
or
100 = 1 / Ib (substitute known values)
or
100 * Ib = 1 (move the Ib over to the left)
or
Ib = 0.01A (move the 100 to the right)

Now solving for resistor needed with Ohms Law:
V=IR
or
(5 - 0.8) = 0.01 * R (substitute known values - factoring loss via transistor)
or
4.2 = 0.01 R (simplify V)
or
420 = R (move 0.01 to the left)

Viola! You need a 420 ohm resistor connected between the base and mCu pin.

To see in action: Falstad.com Circuit Simulator (A word of caution: need Java to run)

With a 420 ohm resistor:

With a 1k ohm resistor (for comparison). Notice Ie is only 431.5mA.