Haha of course. I knew the law but somehow didn't make the connection .. ohms law .... I is inverse to R, so smaller R = more current. Great!
Is it a little more complex to work out for this circuit exactly, as its AC? Would we not need the impedance calc for it, or does it simplify? Please forgive the low level questions, this is all what I am working through right now
In general, we are going to treat an AC source using its RMS voltage and internal impedance. We want the Thevenin equivalent source. We may not be able to get at the inductance value very easily but we can still look at voltage droop versus load current and come up with an equivalent internal resistance.
Yes, everything about AC is a lot more difficult. Part of the reason is that impedance has a component that varies with frequency (reactance, inductive or capacitive) and we inevitably wind up with complex numbers when we want to draw the impedance on an X-Y (or R-X) plane (although sometimes we use magnitude and angle - not a vast improvement!). Next up, we want to look at the transient (step) response and that tends toward differential equations (DEs)and then we get into Laplace Transforms because it is a markedly easier way to solve DEs.
Once you leave DC circuits, the math gets a lot deeper. Even DC circuits can be pretty ugly and require matrix algebra for the solution.
I don't want to scare off the hobbyists, there are a lot of fun things to do that don't require much more than Ohm's Law. Even op amp circuits can be analyzed with little more than Ohm's Law and Kirchoff's Current Law.
The Art of Electronics (and the companion lab manual) try to reduce the math and that's a very good thing. OTOH, tools like Matlab and wxMaxima make the entire EE program much more approachable. I was still using a slide rule when I graduated. The HP35 had JUST been invented and it was well out of my price range.