As Bill pointed out, there is a flaw in the above calculations. One can't just choose an arbitrary voltage drop to assign to the resistor. The actual drop across each resistance will depend on the current, which must be calculated using the total resistance of the circuit (including the motor, not just the resistor alone) and the battery voltage.
Electrical concepts are often explained using the flow of water through a hose as an analogy (as if fluid dynamics were simpler). A certain amount of water will flow through a hose (current) at a given source water pressure (voltage) and a given amount of friction or restriction (resistance) within the hose. No matter how many restrictions there are to the flow (e.g. crimping the hose or putting a valve in the hose or running a hydraulic motor), the amount of water coming out the end must be the same as the amount going in at the spigot. The water can't build up or disappear anywhere within the hose, so the flow has to be constant throughout the hose. That's the "equality of currents".
That same flow creates heat due to friction at the crimp or valve in the hose and produces the motion of the hydraulic motor. Both the valve and the motor also create pressure drops within the hose at their exits, since some of the energy was used in creating the heat and motion. The pressure at the end of the hose, at the point it meets the atmosphere, is zero. One can also picture a battery (or generator) as a water pump in this analogy.
Does this help explain the concept, or am I all wet and tempting fate by mixing water and electricity?
