Hi Sunny. I don't mean to sound rude and not entertain your comments but your demo is more advanced than what I currently understand. It'll take me some time to unpack your response but I really appreciate the exposure!

I don't fully understand the conclusion of your second example (the computed power will be -10 Watts). A square wave signal that reverses polarity won't change the fact that the 10-ohm absorbs power (Watts > 0).

Can you elaborate why p[n]≠i[n]*v[n]? it seems like reasonable extension of p(t)=i(t)*v(t) when t=nT with sampling interval T.

Intuition tells me that you only need to sample as fast as needed to resolve the features that you're interested in seeing on the voltage or current signal (e.g., if current or voltage oscillates at startup (causing your sensor to behave erratically) and you want to figure out the cause, you'd need to sample faster than twice the frequency of oscillation).

It sounds to me like he's trying to design a battery-testing circuit without knowing what to measure. A battery-testing circuit should test that it meets battery specifications (charge time, peak/nominal discharge rate, cell voltage vs. current draw curve, self-discharge rate, etc.). The author of this question should specify which battery specifications he's testing. He said he's not sure what calculations are needed -- well, what is he trying to calculate? Or is he asking what information about a battery can you measure with current vs. time information?

@JRobert What debugging tools do software developers working in a multi-threaded environment (in a hardware setting where the use of Logic Analyzers and oscilloscopes isn't practical) have?

Ah. So how the conductor is shaped and where the electrical connections (in/out) are physically located determines the where the majority of the current flows. The facts to reconcile are: (1) Current flows through the large/infinite number of paths in parallel (2) The sum of the current going into the conductor across all paths must equal the sum of the current coming out of all paths (3) The larger the conductor and if voltage is kept the same, the smaller the sum of current through all paths.