P=E*I

Voltage : is the electromotive force (pressure) applied to an electrical circuit measured in volts (E).
Current : is the flow of electrons in an electrical circuit measured in amperes (I).
Resistance : is the opposition to the flow of electrons in an electrical circuit measured in ohms (R).
Power   : is the product of the voltage times the current in an electrical circuit measured in watts (P).
Ohm's Law
In its simplest form, Ohm's law states that the current in an electrical circuit is directly proportional to the applied voltage and the resistance of the circuit. The 3 most common mathematical expressions are:
E=I*R   I=E/R   R=E/I

Also, the power can be expressed as P=E*I and with a little algebra we can combined these expressions and derive P=E² / R

So what does all this mean? Well, for one thing it becomes clear that an appliance (load) that draws 1 amp (ampere) of current at 120 volts will draw 10 times as much current at 12 volts (1/10 the voltage) or 10 amps. Since P=E*I then 120 volts times 1 amp = 120 watts. Also, 12 volts times 10 amps = 120 watts. So you can see that the power remains the same. As the Voltage goes down, the Amperage increases to maintain the power which will be determined by the 3rd factor, resistance.

Ok, now let's say you have a nice 1200 watt hairdryer. Well, that would work out to 10 amps at 120 volts. But, when your power inverter uses the 12 volts supplied from your batteries, the amperage goes up to 100 amps to produce the same 1200 watts! (P=E*I). This means that even the very large cables connecting your batteries to the inverter will get warm. This is why it becomes impractical or impossible to run say, a 4000 watt electric clothes dryer. Even if you had large enough wires to handle the required 333 or so amps, your batteries would not last long.

It is true that the cables will not get as warm if the current can be reduced by increasing the voltage by using a 24 volt battery system or even a 48 volt battery system. This still will not change the amount of power that your batteries must supply.
The 12 basic formulas for Ohm's Law can be expressed as follows :
A graphic representation of 12 variations of Ohm's Law
  1. Voltage = the Square Root of Power * Resistance
  2. Voltage = Power / Current
  3. Voltage = Current * Resistance
  4. Resistance = Voltage / Current
  5. Resistance = Power / Current squared
  6. Resistance = Voltage squared / Power
  7. Current = Voltage / Resistance
  8. Current = the Square Root of Power / Resistance
  9. Current = Power / Voltage
  10. Power = Voltage * Current
  11. Power = the Current squared * Resistance
  12. Power = the Voltage squared / Resistance
You will primarily be interested in just formula number 10 : P=E*I   (watts = volts * amps). With this single formula, you can determine the wattage a device uses by multiplying the Voltage in Volts times the Current in Amps.
Summary
The upshot of all this is twofold:

1) You will need to replace electric appliances that need large amounts of power with gas (natural or LP) or other alternatives. This would usually be anything that uses 1500 watts or more. All appliances that are UL rated will have their power consumption in watts listed on a placard or label near the AC cord.

2) When you find the wattage listing you can divide by 120 to get the number of amps the appliance will require. Multiply this number by 10 for a 12 volt system to determine the number of amps that will be drawn from the batteries. For a 24 volt system, multiply by 5. For a 48 volt system multiply by 2.5.
 

 

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