1) understanding current
See Measure Current with Multimeters and DC Circuits for a hands on example.
Arbitrary example: Draw 100uA(u isengineering notationshorthand for micro, 1 millionth(1e-6) of an Amp)
from a 1.5V battery.
Solution: Solve Ohms law for a resistor value that will cause 100uA to flow from the battery... V=IR and you are given V and I. Move the "I" over the equals sign(aka move across the equality) to get V/I = R.
For this simple example you could just plug in the numbers immediately, but leaving everything in variable form allows things to be changed or recalculated easier if necessary. 1.5V/100uA = 15000 Ohms or 15kOhms using engineering notation.
I had significant trouble understanding V=IR, a remarkably simple equation, because I didn't understand current. A battery has a voltage and a resistor has a resistance, but then there was this current thing that came from somewhere for some purpose. I didn't understand how to apply and use a formula because as a high school student and into college I was used to working with formula's in math that had little or no meaning from a problem solving perspective. Law's like Ohms law are based on significant history and accurately model a real event. I was resistant to the fact that current could be that simple because I didn't understand how it applied to anything. What was fuzzy for me was that voltage and current show up on power supplies everywhere and it's rare that the circuit is an actual resistor network, more on this soon.
Things were more confusing for the range, scope and scale of everything. I didn't understand basic principles on the practical side of what you can and can't do, what typical values were and how to select values. Most of this came with experience as I worked through circuit problems and projects. What's "typical" depends on what branch of the field of electrical engineering you are working in/on. What's practical depends on design considerations: Power(which considers voltage and current), Area(space), and Speed(how fast does this need to run).
The amount of current flowing depends on the individual circuit. If you are working on out door power lines then you are dealing with thousands of Amps. If you are working on mixed signal Integrated circuits(AKA "computer chips" even though they might not be a computer) typical values are in the microAmp(1e-6, "u") to milli-amp(1e-3,"m") range.
I didn't understand the waterfall analogy and it still doesn't really work for me. It wasn't until I worked with a power supply, multi-meter and a resistor in series with a motor at my first co-op that the relationship finally clicked. Seeing the current draw from the power supply vary directly, and predictably, as the voltage or resistance changed caused everything to click. It was a realization that things DO follow Ohms law and it's not just some oversimplified formula that has no practical application in "the real world"!
