I have seen a fair amount of confusion with different voltages and the effects on equipment. Let us do ohm law because that is the easiest and is directly applicable to resistive loads.

RESISTIVE LOADS only.
I = E/R
Keeping the resisance constant at 6 ohm for example

On 6 volt I = 6 /6
= 1 amp

12 volt I = 12 / 6
= 2.0 amp

POWER
P = I x E or I squared R

on 6 volt
P = 6 x 1
= 6 watt

on 12 volt
P = 12 x 2
= 24 watt

So power goes up by the square of the voltage change. For this reason you have to select dropping resistors carefully. As one has seen too small a wattage and they burn out.

MOTORS
Here is where things get complicated they obey ohms law but then there are other factors.
HP = 746 watts
HP = (Torque x RPM) divided by 5252

First let us do AC motors since someone mentioned them. A common motor is one for 115 or 230 single phase. Yes it will run PROPERLY CONNECTED on higher or lower voltage. What they do is on low connection the windings are in parallel
SO for a 1 HP motor drawing 746 watts for the 115 volt connection each winding is drawing 373 watt, connected in parallel across 115 and drawing approx 3.24 amp. Since they are in parallel Line current is the total of current and is 6.28 amp.

HIGH VOLTAGE connection each winding is still drawing 373 watt, 3.24 amp and at 115 volt BUT they are in series so the voltage across the two is 230. Line current is now 3.24 amp.

The same holds for 3 phase dual voltage motors. You save almost no power with either connection except for line current drop. Where you do save with the higher voltage is wire size and starter size which are definitely cost factors.

DC motors. One person asked why can DC motors operate on PWM power supplies at a lower voltage (and speed).

ANY DC motor can be operated at a lower voltage. This is the oldest trick in the book of motor control. Halve the voltage and roughly halve the speed and half the current as explained below.

Yes you can run 6 volt motors on 12 volt
PROVIDED
1. The insulation can take it
2. Torque. Let us assume a constant torque load - this is almost anything on wheels cars trains conveyers etc etc.

This does NOT apply to pumps or fans. They obey another confusion factor the affinity laws. Basically on a centrifugal pump or squirrel cage fan double the speed and power goes up by 8.

3. You do not overspeed it and throw windings out of the armature.


For constant torque loads torque does not change with speed. HOWEVER HP will be proportional to speed
HP = T x RPM /5252. Double RPM then double HP. HP = 746 watts so running a motor at double voltage will double wattage and about double amperage. If the motor can keep itself cool you are OK.

The reason you can get away with this is Counter Electro Motive Force aka generator action
ALL MOTORS ARE GENERATORS AND
ALL GENERATORS ARE MOTORS
The generator action in a motor produces CEMF - this opposes the line voltage and reduces the "actual motor voltage". You cannot directly measure this but can get an idea of it. CEMF is proportional to motor speed so if you run at double the design volage and double the speed the increased CEMF will save you by lowering the actual motor run voltage thus current.

All bets are off with a hard startig engine though - I predict a new starter motor if you do this every day.

Take a DC motor and measure resistance line to ground or line to line. Let us say it is a starter motor - I would estimate resistance at about 0.1 ohm or so. At 12 volt this will draw about 120 amp - which if you have a high range curren meter you can see. The motor is not up to speed thus CEMF is low and is zero at start Once the motor speeds up the current drops to let us say 30 amp (not a very big starter motor).

So at speed "run voltage = I x R
= 30 x 0.1
= 3
Therefore CEMF = 9.

You can also see this directly
Take a motor and if you have a variable DC power supply slowly crank the voltage up and watch the current rise. Once the motor starts turning it is generating CEMF and you will see current drop like a rock.

Dan Bentler