Okay, but my issue was really with the use of the word "entering" in the question. I mean, power doesnt "enter" a battery while it's discharging. It doesn't really "enter" the resistors either, but that made more sense to me at the time. It just seems like quite a non-intuitive use of language.

But anyway, other than that I think the whole thing works pretty nicely. I'm sure the discussion area will liven up as the course goes on, too.

You really have to think of it this way in engineering, otherwise energy balances will mess up your day.

Power enters the resistor as electrical energy (and leaves the resistor as heat). If you draw a control envelope around the resistor then an energy balance is satisfied: power in minus power out equals rate of accumulation of energy in the resistor.

Electrical power leaves the battery while it is discharging, which means, according to the chosen sign convention (power entering has a positive sign), that power leaving the battery has a negative sign. If you draw a control envelope around the battery, then again an energy balance is satisfied: power in minus power out equals rate of accumulation of energy in the battery. In this case power in is zero, power out is positive, meaning the rate of accumulation of energy in the battery is negative--the battery is losing energy to the circuit. Specifically, the battery has a store of chemical energy which is being depleted. In engineering you always have to remember the sign of each term, as a wrong sign is another thing that will mess up your day.

If you now draw a control envelope around the whole circuit and consider only electrical energy, then the power leaving the battery (negative sign) is exactly balanced by the power entering the resistors (positive signs). The sum of these is zero. Which means in effect that the chemical energy in the battery is being converted to heat energy in the resistors with the electricity acting as the transfer medium. This "electrical energy balance" only works because there are no other ways the circuit can generate electrical energy or dissipate electrical energy or accumulate electrical energy. If, for example, the circuit could radiate energy as electromagnetic waves then the balance would need to be extended to be complete. That's the last thing in engineering that will mess up your day: making the wrong assumptions about which terms to include and which terms can be neglected.