Hi Scott,
What you have are four quantities, all inter-related:
Voltage. Symbol E, measured in Volts. This is the electrical "pressure" which acts upon the electrons. You can liken it to the applied pressure in a water pipe.
Current. Symbol I, measured in Amperes (amps). This is the rate, or speed, at which electrons are flowing in the circuit.
Resistance. Symbol R, measured in Ohms. This is the degree of resistance offered by the mnaterial through which the current is flowing.
Power. Symbol P, measured in Watts. The is the actual amount of energy which is being dissipated, or used up, in the circuit. It may be energy which is radiated as heat or light, or used to create motion, as with an electric motor.
Now.....
Ohm's Law states the relationship between voltage, current, and resistance. Current is directly proportional to voltage and inversely proportional to resistance, or in mathematical terms:
I = E / R (Current = Voltage / Resistance)
Think back to water-in-a-pipe analogy. If you increase the pressure behind the water, the rate of flow will increase. This happens in an electrical circuit too: If you increase the voltage (pressure), then the current will increase proportionally.
If you kept your water pressure constant but changed the pipe for a smaller one, the flow rate would be reduced. Similarly, in an electrical circuit if you kept the voltage the same but increased the resistance, the current would be reduced.
See where we're going with this? Let's take an example, and say you had a 12V battery connected to some device which had a resistance of 6 ohms. By Ohm's Law, the current would be:
I = E / R = 12 / 6 = 2 amps.
If you substituted a device which had a resistance of, say, 3 ohms, then the current would increase:
I = E / R = 12 / 3 = 4 amps.
With that lower reistance, the only way to get the current back down to 2 amps would be to reduce the voltage to 6V, thus:
I = E / R = 6 / 3 = 2 amps.
See how the quantities are related? You can't change one without affecting one of the others.
Now on to power. The power is proportional to both the current and the voltage:
P = I x E
Clearly then, anything which changes either voltage or current will affect the power. In the above example of a 12V battery feeding into a resistance of 6 ohms, we've seen that the current is 2 amps. The power, therefore, is:
P = I x E = 2 x 12 = 24 watts.
Now, to get to your point about how you can have high power with a low current, let's take a practical power-line example. Suppose you had an electric heater in your home running on 120V and rated at 1200W. The current would be 10 amps, because:
P = I x E = 10 x 120 = 1200W.
If you had a 1200W heater designed to run off 240V, you would get the same amount of heat (power) from it, but the current would be only half:
P = I x E = 5 x 240 = 1200W.
See how we've doubled the voltage, but halved the current, so the power stays the same?
The reason that the 240V heater only draw half as much current as the 120V version is that its resistance is much higher.
Rearranging the Ohm's Law formula, you can work out the resistance of each:
R = E / I = 120 / 10 = 12 ohms
R = E / I = 240 / 5 = 48 ohms
That four-fold difference in resistance is why the higher voltage in the second example results in a lower current, yet in both cases the power is the same.
