# Can voltages be different if watts are the same? Does DC vs. AC change this?

I'm currently building a home in a van, it's my first tango with electrical engineering. I watched a video on voltages and amps and my understanding is basically like so: a battery is like a water tower, voltage is the pressure, amperage is the size of the pipe, and watts is how much water comes out per second.

So now I'm wondering what the big deal with amperage and voltage is when it seems matching wattage should be enough. If a motor were a water wheel, it shouldn't matter whether it's water rushes through a small canal or lazily passes by in a large creek so long as the amount of watt-er per second is the same... or so I imagine.

Does AC vs DC have something to do with this? Certainly the moving water metaphor totally breaks down there.

{And, in the context of my project, my current plan is 12V DC (car battery) -> 12V DC to 15V AC (inverter) -> 15V AC to 15DC (Mac Book Pro charger [which I think is a converter]) -> 15V DC input on computer... in the end it seems like my mac just wants x amount of watts.}

• Are you sure your charger accepts 15Vac and not 115Vac or 120Vac? – 2012rcampion Jan 16 '15 at 6:04
• Re-re-re-re-check Macbook voltage required. About zero chance of it being 15 VAC. – Russell McMahon Jan 16 '15 at 8:54
• Ever used a water pressure washer? It isn't really that much water coming out (current), but it cleans the ground much better than dropping a container of the same amount of water just on the floor... – PlasmaHH Jan 16 '15 at 11:17
• I think so.. check this image out – Thumbz Jan 16 '15 at 21:23
• and I had no intention of risking my 2PC, but I would make an awful engineer if I simply accepted having a system with so many conversions – Thumbz Jan 16 '15 at 21:32

Just to correct your water analogy:

The Voltage is the water pressure, The Current is the flow The multiplication of Voltage and Current is the power and it is the same with water, the product of flow and pressure is the hydraulic power:

If you have a pump running in a pool of water just recirculating you have flow (current) but no pressure (Voltage) and no power. It is not doing any useful work.

If you have a pump running with a valve on its outlet that is closed there is pressure (Voltage), behind the valve, but no flow (current) and no power. Again, no useful work.

It is only when you have flow against a pressure that useful work gets done. Like when you pump water up to a high mounted tank, no so high that the pump can't do it!

To get a clear picture electrically: A 1.5 V dry cell battery sitting on the desk has a voltage between its terminals but no current flow, since there is no circuit for the current to flow in. There is no power - no heat or anything. Power = 1.5 x 0 = 0.

Connect a 0.5 W 1.5 V 0.33 A light globe and current flows and there is power! Since the wire in the globe is the right size to carry 0.33 A at 1.5 V, the Power is 1.5 x 0.33 = 0.5 W and it gives out light (and heat) the total of which is 0.5 W.

The water flow analogy can even be used for alternating current but that is another story...

Wattage is only about power consumption; it's the product of voltage and amperage. You can't just set wattage.

Well, understanding ohms law is a good place to start. It's usually written as:

V = IR

V = voltage I = current R = resistance

If, for example, you have a heater that is designed to pull 5 amps of current at 120 volts, if you hook it up to 240, it is now going to pull 10 amps of current. That will very likely burn it out. This is definitely true of your MacBook; if you send it too high a voltage, you will burn it out.

Ohms law works correctly with resistances, but isn't quite accurate when you are dealing with motors or power supplies for electronics.

For your project, you are unlikely to be able to find a 15VAC inverter. Your choices are to go from 12VDC to 120VAC and then use a standard power supply to go to the 15VAC your MacBook needs. Or, you could get what is known as "boost" converter that can go from 12VDC to 15VDC directly. That would be more efficient, but less flexible since it could only power the laptop.

First, three definitions:

• Current (measured in Amperes, or Amps) is a measure of how much charge is moving through a wire.
• Voltage (measured in Volts) is a measure of the potential in a wire (pressure in the water analogy).
• Power (measured in Watts) is a measure of how much energy is moving through a wire

(Note that $1\text{ Watt} = 1\text{ Volt}\times 1\text{ Amp}$)

Second, the difference between AC and DC current:

• DC current is a steady flow, like a river. This is the type of current that batteries produce.
• AC current sloshes back and forth at a specific frequency, and for technical reasons is easier to convert to high voltage. It is the type of electricity used in the power grid.

Note that while AC/AC conversion (at the same frequency) are very easy, AC/DC conversion is a little harder, DC/DC conversion is pretty hard, and good DC/AC conversion is very hard.

Now I think a worked example might make your question a little clearer.

My laptop consumes up to $2.1\text{ A}$ of current at $19\text{ V}$, or $2.1\text{ A}\times 19\text{ V}=40\text{ W}$ of power. The AC charger must then convert at least $40\text{ W}$ of power. At the mains voltage of $115\text{ V}$, the amount of current it consumes is at least $40\text{ W}/115\text{ V}=0.35\text{ A}$.

Practically, it will consume a bit more than the laptop does since some power is lost in the conversion process. (Lost as heat, which is why the power brick gets warm.)

The reason we care about the different voltages and currents is convenience. More current requires a larger wire (pipe) to handle it. On the other hand, high voltage (pressure) can be dangerous because it needs more insulation (thicker pipe wall) to prevent arcs (sparks) from forming.

You also need to make sure that the voltage and current of the source and device match. A device which is expecting higher voltage may not run, or worse, run incorrectly and be damaged (think of what happens if you lose oil pressure in your car). A device which is expecting lower voltage can be overloaded by a high voltage source.

So, if your laptop expects $15\text{ V}$ DC, then you should make sure to provide it with $15\text{ V}$ DC. As long as you have the correct voltage and enough current to spare, you will be ok.

Now if you are just powering your laptop off the car battery, it will be much more efficient to use a DC/DC converter designed for the task. However, if you will be powering other household devices from your battery, you should get a DC/AC converter (called an inverter). Remember when I said that DC/AC conversion is hard? A good inverter that will provide good quality power is probably going to be expensive, but buying a cheaply made one could damage your devices.