Maybe this will help with the "time" or "rate" question. The unit you are speaking of, the watt, is a unit of power. Power is energy per unit time. 1 watt is 1 joule per 1 second. So time is "built into" the "watt". That is, the watt is, by definition, a rate. If you are dissipating 1 watt for 1 second you 'use' 1 joule, 1 watt for 2 seconds = 2 joules. The utility company is technically charging you for energy usage. The unit is typically a kW hr - a larger unit than a joule, i.e. 50 KwH = 180000000 joules. Why is any of it important other than the electric bill? Think of energy as heat, that is what the big deal about power really ends up at in electronics.