Dave,
I know I’m not Bruce but I think this answers your question.
First, my assumptions:
1) The 12V motor does the same work as the 6V motor (i.e. it spins a fan/moves air at the same speed).
2) If the motors do the same work, the power consumption will be the same. (This is probably not entirely true in reality due to lots of variables but close enough to approximate here.)
3) The resistor(s) are switched in series with the motor to give the motor multiple speeds.
Next, if the 6V and 12V motor power consumptions are the same, this means electrically they consume the same wattage.
Ohm’s Law converted for power is: Watts (W) = Volts (V) X Current (A)
Doubling the voltage (from 6V to 12V) halves the current required to produce the same work (wattage):
Example: Wattage = (6V) x (1A) = 6W = (12V) x (0.5A)
Switches are not really susceptible to voltage variations (especially differences as small as 6V). Voltage failure in switches occurs when you approach the design limits of the internal parts (i.e. switch will arc internally, arc to ground, dielectric breakdown, etc.). We’re talking hundreds of volts or more usually.
However, current limiting capacity (usually the size of the switch contacts/wiring) is the greatest concern – they must be able to handle the current required by the circuit.
Since 6V motors need double the amperage of a 12V motor to do the same work, you can usually assume anything wired for 6V will handle the current needed for 12V operation. Therefore, as long as your 6V switch can handle the same or more current than your 12V motor draws, you’ll be fine.
Lastly, the resistors placed in the motor switch circuit for speed control work as follows:
Electrically, current flow sees the motor as a resistor (which just happens to dissipate energy by rotation rather than purely heat). The voltage is distributed across both the motor and the resistor in proportion to their individual resistances, effectively dropping the voltage and the current across each. The partial voltages across the resistor and the motor will sum to 12V and individually always be less than 12V. This causes the motor run slower than a motor without a resistor because the voltage and current across it will be lower. Further, a circuit with the resistor will draw less current than one without. Therefore, your resistors won’t generate as much heat during 12V operation vice 6V due to less current flow which means they shouldn’t be damaged.
Bottom line, make sure your switch/resistors can handle the max rated current draw of the 12V motor and you’ll be fine.
Dan
(Hopefully any simplifications I made here for clarity don’t confuse anyone…)