Amps, Volts, Watts, Ohms
ohm ... watt amp volts?

I   
can never remember the difference between watts and amps so I am making this page so that when I forget I can just read it again. (No Lie ;o)

Watts = Volts x Amps

Watts is a unit of power having the dimensions (energy per unit time):
M L2 / T2 divided by T = M L 2 / T 3
Note: A kilowatt-hour is a 1000 watts times one hour = an energy unit.

Volt is a unit of force (F=ma):

ML / T2

So that Amps have the dimensions:

L / T

Now, this is a velocity? What is going on here? This begs some explanation.

I was unable to find an explanation on the web after two hours of searching. There are too many documents on the web with the same "overview" type information. So I did what I usually do & figured it out myself.
The true "dimension" of amperage is, of course, 1 / T , i.e. "x" number of electrons pass through a wire in so many seconds. The extra L we need to make power (ML2T -3) is the length of the wire which is left out of the calculation because it is held "constant" for the pupose of teaching. So if you screw in a 100 watt bulb the little filament in the bulb is a constant as is the length of your household wiring. Now if you increase the length of the filament ( - + - ) you increase the wattage of the bulb (like screwing in another 100 watter) ... but ... if you put two filaments together ( = ) you get less resistance instead of more wattage. And less resistance means lower wattage.

The complete equation for watts is:

Watts = Volts x Amps x k(one unit length of wire)

If you have a current running in some wire, it has some length ... get it? ... but since this is true in any case whatsoever, why put it in the equation? So, if I double this "any" length, does the power consumption go up to double? Yes, even if there is no light bulb on it ... but the amps and volts remain the same? Yes, the voltage will remain the same ... if you're talking about the power company. They will ramp up their power output to match demand. If too many people put too much "extra lengths" in the circuit ... and they can't ramp up ... you get a "brown out" which is, lowered voltage.

Note 6/27/02:
There is a mistake here in what follows (pointed out by "Wimms" on my D-Board in June 2002). I can't remember what I was thinking at the time but there is no drain on the system if it adds another "branch". There will be an extra drain on the system if it extends its length to a place where energy is being tapped. It would lose energy to an unused branch only do to leakage which is minor and not a logical part of the problem. Also, I don't know if maintaining an alternating current voltage consumes energy which would make the error correct again for the wrong reason. I will find out when I get back from vacation.). Certainly, a direct current would not, as would be the case with a simple unused battery (which just leaks away).

Incorrect:
If the power company adds a line to its system (say, to a new subdivision) they must increase their power output to maintain the 115 volt standard even if no one is yet in the subdivision using power ... because ... the extra wiring is resistance of and unto itself, i.e. it gets "hot", like ... warm. The power company's system is a big electric heater even in its "wait state", i.e. waiting for some customer to use it.

If everyone flushes the toilet at the same time, the water pressure goes down ... unless the water utility "pushes" it harder. They can't reasonably do this (they would need a variable height water tower), but the electric company can.

So when you turn on your lamp (add a length of wire), the voltage goes down but the power company puts it right back up to 115V, see?.

So the real, true, actual formula for watts is in fact:

Watts = Amps x Volts x Length
provided that we alter the variable length measurement to reflect a "constant crossection", i.e. a .1 mm filament 2 cm long = 1/8 inch filament very much shorter. But nobody cares about these things except the professionals and people like me who demand that "dimensions cancel out" on both sides of an equation. ;o)

Ohms = Volts / Amps

Ohm is a measure of resistance to electrical conduction.
It is also the way in which prisoners in medieval dungeons resisted their captors. What they did was to find the resonant frequency of their dungeon and hum it. When one guy got tired of humming another prisoner picked it up. The jailers couldn't tell where it was coming from so they were subjected to this constant drone "Ohmmmmm ... ohmmmm ... ohmmmm ...". That's why all dungeon movies have humming in the background.

An ohm is also a unit of force (ML/T2). It is the force opposed to the force of the volts which are pushing the electrons through the wire ... like the earth pushes up on your feet while you weigh it down. But unlike the earth, resistance does not push back with an equal force. It gives.

Unfortunately, the formula for ohms is also screwed up in its dimensions. If Ohms = Volts / Amps there is another problem with the amp dimension. As it stands here, the formula indicates that ohms have the dimensions of ML/T which is momentum. We need to divide the left hand side of the equation by "time" to get back to the units of force.

Clearly, if Ohms = Volts we would have our dimensions in order but the quantity of ohms and volts would be equal and the current would not flow. By dividing the volts by some number we obtain a lesser quantity for ohms than we have for volts and the current will flow albeit against some resistance.

The equation shows that the ohms are inversely proportional to the number of amps flowing. This simply reflects experimental observation. So we multiply the amps (1/T) by time (T) to get a pure number under the volts and we obtain a lesser force for the ohm measure.

Voila !

Wait a minute ... "nothing like pulling a rabbit out of a hat" - Rocket J. Squirrel.
"What we have here is a failure to communicate"
Actually, multiplying the amps by time is the hidden component like length was hidden in the watts example. We want to measure the amperage to know the resistance so we have to measure it for some amount of time ... there is no way to measure it instantaneously. That measure of time is "unit time", i.e. one unit of time in the mks or cgs system or any other system of measure. What we're actually putting on the bottom is not amps but amp-seconds ... a pure number (actually Couloumbs but they don't count in the dimensionality game ... at least not the way I play it).

There are many other dipsy-doodle quantities that scientists use to make things come out right mathematically and they are all legitimate. But it's such a pain ... who wants to explain everything all the time? ... that they don't bother to put them down in the equation. It saves time and space just to "throw 'em away" and get on with the essentials.

Lenz Resistance

While I'm at it, there is another type of electrical resistance unlike the ohm. Every changing electric field creates a corresponding changing magnetic field and vice versa. But ... that induced field is always opposed to the original field though of lesser strength. Thus, the growing electrical field, when the switch is turned on, generates a magnetic field which in turn generates another electrical force opposed to the first. There is spring effect here (damped out by generated heat) which bounces the electricity back and forth until equlibrium is reached with the current flowing in the proper direction. This doesn't matter for low amp/volts but with heavy duty power, a power company worker uses a long wood pole to (10 foot long?) to flip the breaker ... just in case.

Also, while I'm at it. You don't have to touch a high tension electric line to get killed. Just get close enough and it'll jump out to get ya'. Those big lines aren't insulated completely because of the weight problem. So the electricity can arc out of the wire just like lightning arcs to the ground. If you want to know how close you can get look at those long string-beaded "thingees" that are attached directly to the wire from the support tower that holds up the line. They are insulators ... there to keep the electricity from "jumping" to the metal tower and into the ground. Usually they're about 3-6 feet long (meaning don't go closer than about ten feet if you value your life).

Note:
As you can see a watt is the indefinite integral of volts with respect to amps and an ohm is the related derivative (the "instantaneous" rate of change of volts to amps).

I guess this is enough stuff to remind me that the difference between a watt and an amp is that a watt can be the same yet be composed of a different quantity of amps provided that we change the volt quantity correspondingly.

Watts = VOLTS x Amps


Anyone interested in physics may go to Google
to see my video "The Nature of Existence"
which was posted there (03/10/2008). Forty six years in the making ;o)


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