I changed what I was going to do today due to student interest.

First, a little background. A student noticed that, if you add the reciprocals of the resistances of a parallel circuit and multiply that by the voltage of the battery, you get the current out of the battery. We also had a question with two resistors in parallel (48 Ω and 12 Ω) in series with another resistor (9.6 Ω). The two resistors in parallel shared the voltage equally with the one resistor, and the sum of the reciprocals of the two resistors (1/48 + 1/12) equaled the reciprocal of the sole resistor (1/9.6). It was as if the reciprocal gods were controlling circuits.

So, after doing some TIPERs today, we tried to figure out why this happened. I showed the proof for the equivalent resistance in series and in parallel, and so many a-ha moments happened. We then did some equivalent circuit problems, and we saw them as cool logic puzzles to solve.