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# HOW ARE WATTS, OHMS, AMPS, AND VOLTS RELATED?

William Beaty
Apr 2, 2000

What's all this about Watts, Volts, and Amps? Good question. Some info is below, and more can be found at ELECTRICITY FAQ, also at Electricity is not energy and Electricity Misconceptions page. But none of these links give a direct answer to the question. Be warned! A useful answer is going to be HUGE! (grin)

Here's the extremely short answer...

Conductive objects are always full of movable electric charges, and the overall motion of these charges is called an 'electric current.' Voltage can cause electric currents because a difference in voltage acts like a difference in pressure which pushes the conductors' own charges along. A conductor offers a certain amount of electrical resistance or "friction," and the friction against the flowing charges heats up the resistive object. The flow-rate of the moving charges is measured in Amperes. The transfer of electrical energy (as well as the rate of heat output) is measured in Watts. The electrical resistance is measured in Ohms. Amperes, Volts, Watts, and Ohms.
Not so simple? Then let's take a much deeper look. First the watts and amperes. Watts and amps are somewhat confusing because both are flow-rates, yet we rarely talk about the "stuff" which does the flowing. I suspect it's impossible to understand a flow rate without first understanding the substance which flows. Take water flow for example, could we really understand gallons-per-second, if we didn't understand gallons, and we had never touched water? It's not easy to understand flow rates like Amperes or Watts without understanding the "flowing material." First let's do the Amperes.

```
Since a current is a flow of charge, the common expression
"flow of current" should be avoided, since literally it means
"flow of flow of charge."
-Modern College Physics. Sears,Zemanski,Richards,Wher
```

Current isn't a stuff. Electric currents are the flows of a stuff. OK then, what's the name of the stuff that flows during an electric current? The flowing stuff is called "Charge."

## AMPERES

A quantity of charge is measured in units called COULOMBS, and the word Ampere means the same thing as "one Coulomb of charge flowing per second." If we were talking about water, then Coulombs would be like gallons, and amperage would be like gallons-per-second.

What flows inside wires? It has several names:

• Charges of electricity
• Electrons
• Charged atoms (ions in salt water etc.)
• Electric charge
• Electrical substance
• The Electron sea
• The ocean of charge
• Electric fluid
• "Charge-stuff"
Why are Amperes confusing? Simple: textbooks almost always teach us about amperes and current, but without first clearly explaining the coulombs and charges! Suppose that we had no name for "water," yet our teachers wanted us to learn all about the mysterious flow inside metal plumbing pipes? Suppose we're required to understand "gallons-per-second," but we had to do this without knowing anything about water or about gallons?

If we'd never learned the word "gallon", and if we had no idea that water even existed, how could we hope to understand "flow?" We might decide that "current" was flowing through dry empty pipes. We might even decide that "current" was an abstract concept. Or we might decide that invisible wetness was moving along through the pipes. Or we could just give up on trying to understand plumbing at all. Instead we could concentrate on the math and do extremely well on any physics test, but we wouldn't end up with any gut-level understanding. That's the problem with electricity and amperes.

We only can understand the electrical flow in wires (the amperes) if we first understand the stuff that flows inside wires. What flows through wires? It's the charge, it's the metal's own particle-sea, the Coulombs...

## CHARGE

"Charge" is the stuff inside wires, but usually nobody tells us that all metals are always jam-packed full of movable charge. Always. A hunk of metal is like a tank full of water. Shake a metal block, and the "water" swirls around inside. This "water" is the movable electric charge found inside the metal. In our science classrooms we call this by the name "electron sea," or even "electric fluid." This movable charge is part of all metals. In copper, the electric fluid is actually the outer electrons of all the copper atoms. In any metal, the outer electrons do not orbit the individual atoms. The electrons do not behave as textbook diagrams usually depict atoms. Instead, the atoms' outer electrons drift around inside the metal as a whole.

The movable charge-stuff within a metal gives the metal its silvery metallic color. We could even say that charge-stuff is like a silver liquid. At least it appears silver-colored when it's in metals. When it's within some other materials, the movable charges don't usually look silvery. "Silvery-looking charges" applies to metals, but isn't a hard and fast rule.

Note that this charge-stuff is "uncharged", it is neutral. It's uncharged charge! Is this even possible? Yes. On average, the charge inside a metal is neutralized because each movable electron has a corresponding proton within an atom nearby. Each electron is always fairly close to a proton. The electric force-fields from the two opposite charges cancel each other out. The overall charge is zero because equal quantities of opposite polarity are both present. For every positive there is a negative. But this doesn't mean that the charge-stuff is gone. Even though the average amount of charge inside a metal is cancelled out, we can still cause one polarity of charge to move along while the other polarity remains still. For this reason, an electrical current is a flow of "uncharged" charges. Metal is made of negative electrons and positive protons; it's like a positive sponge soaked with negative liquid. We can make this "negative liquid" flow along.

## ELECTRIC CURRENT

Whenever the charge-stuff within metals is forced to flow, we say that "electric currents" are created. The word "current" simply means "charge flow." We normally measure the flowing charges in terms of amperes.

The faster the charge-stuff moves, the higher the amperage. Watch out though, since amperes are not just the speed of the charges. The MORE charge-stuff that flows, (flows through a bigger wire for example,) the higher the amperage. And a fast flow of charge through a narrow wire can have the same amperes as a slow flow of charge through a bigger wire. Double the speed of charges in a wire and you double the current. Pinch a wire thinner, and the charges in the thin section flow faster. But if you keep the speed of a wire's charges constant, then increase the size of the wire, you also increase the amperes.

Here's a way to visualize it. Bend a metal rod to form a ring, then weld the ends together. Remember that all metals are full of "liquid" charge, so the metal ring acts like a water-filled loop of tubing. If you push a magnet's pole into this ring, the magnetic forces will cause the electron-stuff within the whole ring to turn like a wheel (as if the ring contained a movable drive-belt). By moving the magnet in and out of the metal donut, we pump the donut's movable charges, and the charges flow in a circle. That's essentially how electric generators work.

Electric generators are magnet-driven charge pumps. The changing magnetic field pushes the wire's movable sea of charges, creating the amperes of charge flow, but this can only occur when a closed ring or "complete circuit" exists. Break the ring and you create a blockage, since the charges can't easily escape the metal to jump across the break in the ring. If the charges within the metal are like a drive-belt, then a gap in the ring is like a "brake" that grabs the belt in one spot and stops all belt motion. A complete metal ring is a "closed electric circuit," while a broken ring is an "open circuit."

A battery is another kind of charge pump. Cut a slot in our metal ring and install a battery in the slot. This lets the battery pump the ring's charge-stuff in a circle. Batteries and generators are similar in that both can pump charge through themselves and back out again. With a battery installed in our metal ring, the battery draws charge into one end and forces it out the other, and this makes the entire contents of the metal ring start moving. Make another cut in the metal ring, install a light bulb in the cut, and then the "friction" of the narrow light bulb filament against the flowing charge-stuff creates high temperatures, and the wire filament inside the bulb glows white-hot. The battery drives the ring of charge into motion, the charge moves along like a solid rubber drive belt, and the light bulb "rubs" against the moving charge, which makes the filament grow hot.

Important note: inside wires, usually the charge-stuff flows extremely slowly; slower than centimeters per minute. Amperes are an extremely slow, circular flow. See SPEED OF ELECTRICITY for info.

## WATTS

Watts have the same trouble as Amperes. "Watts" are the name of an electrical flow... but what stuff does the flowing? Energy! A "watt" is just a fancy way of saying "quantity of electrical energy flowing per second." But what is a quantity of electrical energy? I'll get to that in a sec. But briefly, any sort of energy is measured in terms of Joules. A joule of electrical energy can move from place to place along the wires. When you transport one joule of energy through a channel every second, the flow-rate of energy is 1 Joule/Sec, and "one Joule per second" means "one watt." (It might help keep things traight if you erase all the "watts" in your textbook, and instead write "joules per second.)

What is power? The word "power" means "energy flow." In order to understand these ideas, it might help if you avoid using the word "power" at the start. The word "power" means "energy flow", so instead you can practice thinking in terms of energy-flow instead of in terms of the word "power." Also think in terms of joules-per-second rather than watts, and eventually you'll gain a good understanding of the ideas behind them. Then, once you know what you're talking about, you can start speaking in shorthand. To use the shorthand, don't say "energy flow", say "power." And say "watts" instead of "joules per second." But if you start out by saying "power" and "watts", you might never really learn what these things are, because you never really learned about the energy flow and the joules.

## FLOWING ELECTRICAL ENERGY

OK, what then is electrical energy? It has another name: electromagnetism. Electrical energy is the same stuff as radio waves and light. It's made up of magnetic fields and electrostatic fields. A joule's worth of of radio waves is the same as a joule of electrical energy. But what does this have to do with understanding electric circuits? Quite a bit! I'll delve deeper into this. But first...

How is electric current different than energy flow? Let's take our copper ring again, the one with the battery and the light bulb. The battery speeds up the ring of charge and makes it flow, while the light bulb keeps it from speeding up too much. The battery also injects joules of electrical energy into the ring, and the light bulb takes them out again. Joules of energy flow continuously between the battery and the bulb. The joules flow almost instantly: at nearly the speed of light, and if we stretch our ring until it's thousands of miles long, the light bulb will still turn off immediately when the battery is removed. (Well, not really immediately. There will still be some joules left briefly racing along the wires, so the bulb will stay lit for a tiny instant , until all the energy arrives at the bulb.) Remove the battery, and the light bulb goes dark ALMOST instantly.

## AMPERES ARE NOT A FLOW OF ENERGY

Note that with the battery and bulb, the joules of energy flowed one way, down both wires. The battery created the electrical energy, and the light bulb consumed it. This was not a circular flow. The energy went from battery to bulb, and none returned. At the same time, the charge-stuff flowed slowly in a circle within the entire ring. Two things were flowing at the same time through the one circuit. There you have the main difference between amperes and watts. The coulombs of charge are flowing slowly in a circle, while the joules of energy are flowing rapidly from an "energy source" to an "energy sink". Charge is like a rubber drive belt, and electrical energy is like the 'horsepower' sent between the distant parts of the belt. Amperes are slow and circular, while watts are fast and one-way. Amperes are a flow of copper charges, while watts are a nearly-instant flow of electrical energy created by a battery or generator. For a better view of this topic, see WHERE DOES ENERGY FLOW IN CIRCUITS?

But what are Joules? That's where the electromagnetism comes in. When joules of energy are flying between the battery and the bulb, they are made of invisible fields. The energy is partly made up of magnetic fields surrounding the wires. It is also made from the electric fields which extend between the two wires. Electrical-magnetic. Electromagnetic fields. The joules of electrical energy are the same "stuff" as radio waves. But in this case they're attached to the wires, and they flow along the columns of movable electrons inside the wires. The joules of electrical energy are a bit like sound waves which can flow along an air hose. Yet at the same time, electrical energy is very different than sound waves. The electrical energy flows in the space around the wires, while the electric charge flows inside the wires.

## VOLTS

There is a relationship between amperes and watts. They are not totally separate. To understand this, we need to add "voltage" to the mix. You've probably heard that voltage is like electrical pressure. What's usually not taught is that voltage is a major part of static electricity, so whenever we deal with voltage, we're dealing with static electricity. If I grab some electrons and pull them away from a wire, that wire will have excess protons left behind. If I place those electrons into another wire, then my two wires have oppositely-imbalanced charge. They have a voltage between them too, and a static-electric field extends across the space between them. This fields *is* the voltage. Electrostatic fields are measured in terms of volts per distance, and if you have an electric field, you always have a voltage. To create voltage, take charges out of one object and stick them in another. You always do this when you scuff your shoes across the carpet in the wintertime. Batteries and generators do this all the time too. It's part of their "pumping" action. Voltage is an electrostatic concept, and a battery is a "static electric" device.

Remember the battery in the copper ring from above? The battery acted as a charge pump. It pulled charge-stuff out of one side of the ring, and pushed it into the other side. Not only did this force the circle of charges to begin moving, it also caused a voltage-difference to appear between the two sides of the ring. It also caused an electrostatic field to appear in the space surrounding the ring. The charges within the copper ring began moving because they responded to the forces created by the voltage surrounding the ring. In this way the voltage is like pressure. By pushing the charges from one wire to the other, a voltage causes the two wires to become positive and negative... and the positive and negative wires produce a voltage. (In hydraulics we would use a pressure to drive water into a pipe, and because we drove water into a pipe the pressure in that pipe would rise.)

So, the battery "charged up" the two halves of the copper ring. The light bulb provided a path to discharge them again, and this created the flow of charge in the light bulb filament. The battery pushes charge through itself, and this also forces a pressure-imbalance in the ring, and forces charges to flow through the light bulb filament. But where does energy fit into this? To understand that, we also have to know about electrical friction or "resistance." Also: What is Voltage?

## OHMS

Imagine a pressurized water tank. Connect a narrow hose to it and open the valve. You'll get a certain flow of water because the hose is a certain size and length. Now the interesting part: make the hose twice as long, and the flow of water decreases by exactly two times. Makes sense? If we imagine the hose to have "friction", then by doubling its length, we double its friction. (The friction always doubles whether the water is flowing or not.) Make the hose longer and the water flows slower (fewer gallons per second,) make the hose shorter and the reduced friction lets the water flow faster (more gallons per second.) Now suppose we connect a very thin wire between the ends of a battery. The battery will supply its pumping pressure (its "voltage"), and this will cause the charge-stuff inside the thin wire and the charge-stuff within the battery to start moving. The charge flows in a complete circle. Double the length of the wire, and you double the friction. The extra friction cuts the charge flow (the amperes) in half. The friction is the "Ohms," it is the electrical resistance. To alter the charge-flow in a circle of wire, we can change the resistance of our piece of wire by changing its length. Connect a long thin wire to a battery and the charge flow will be slow (low amps.) Connect a shorter wire to the battery and the charge will be faster (high amps.) But we can also change the flow by changing the pressure. Add another battery in series. This gives twice the pressure-difference applied to the ends of the wire circle... which doubles the flow. We've just discovered "Ohm's Law:" Ohm's law simply says that the rate of charge flow is directly proportional to the pressure difference, and if the pressure goes up, the flow goes up in proportion. It also says that the resistance affects the charge flow. If the resistance goes up while the pressure-difference stays the same, the flow gets LESS by an "inverse" proportional amount. The harder you push, the faster it flows. The bigger the resistance, the smaller the flow (if the push is kept the same.) That's Ohm's law.

Whew. NOW we can get back to energy flow.

## VOLTS, AMPS, OHMS, ENERGY FLOW

Lets go back to the copper ring with the battery and bulb. Suppose the battery grabs charge-stuff out of one side of the ring and pushes it into the other. This makes charge start flowing around the whole circle, and also sends energy instantly from the battery to the light bulb. It takes a certain voltage to force the charges to flow at a certain rate, and the light bulb offers "friction" or resistance to the flow. All these things are related, but how? (Try bicycle wheel analogy.)

Here's the simplest electrical relation: THE HARDER THE PUSH, THE FASTER THE FLOW. "Ohm's Law", can be written like this:

```
VOLTS/OHMS = COULOMBS/SEC       The harder the push, the faster
flows the charge
```
Note that coulombs per second is the same as "amperes." It says that a large voltage causes coulombs of charge to flow faster through a particular wire. But we usually think of current in terms of amps, not in terms of flowing charge. Here's the more common way to write Ohm's law:
```
VOLTS/OHMS = AMPERES            Voltage across resistance causes current

```
Voltage divided by resistance equals current. Make the voltage twice as large, then the charges flow faster, and you get twice as much current. Make the voltage less, and the current becomes less.

Ohm's law has another feature: THE MORE FRICTION YOU HAVE, THE SLOWER THE FLOW. If you keep the voltage the same (in other words, you keep using the same battery to power your light bulb), and if you double the resistance, then the charges flow slower, and you get half as much current. Increasing the resistance is easy: just hook more than one light bulb in a series chain. The more light bulbs, the more friction, which means that current is less and each bulb glows more dimly. In the bicycle wheel analogy mentioned above, a chain of light bulbs is like several thumbs all rubbing on the same spinning tire. The more thumbs, the slower the tire moves.

Here's a third way of looking at Ohm's law: WHEN A CONSTANT CURRENT ENCOUNTERS FRICTION, A VOLTAGE APPEARS. We can rewrite Ohm's law to show this:

```
AMPERES x OHMS = VOLTS          A flow of charge produces a voltage if
it encounters resistance
```
If resistance stays the same, then the more current, the more volts you get. Or, if the current is forced to stay the same and you increase the friction, then more volts appear. Since most power supplies provide a constant voltage rather than a constant current, the above equation is used less often. Usually we already know the voltage applied to a device, and we want to find the amperage. However, a current in a thin extension cord causes loss of final voltage, and also transistor circuits involve constant currents with changing voltages, so the above ideas are still very useful.

But what about joules and watts? Whenever a certain amount of charge is pushed through an electrical resistance, some electrical energy is lost from the circuit and heat is created. A certain amount of energy flows into the "frictional" resistor every second, and a certain amount of heat energy flows back out again. If we increase the voltage, then for the same hunk of charge being pushed through, more energy flows into the resistor and gets converted to heat. If we increase the hunk of charge, same thing: more heat flows out per second. Here's how to write this:

```
VOLTS x COULOMBS = JOULES       It takes energy to push some charge
against the voltage pressure
```
Charge flows slowly through the resistor and back out again. For every coulomb of charge that's pulled slowly through the resistor, a certain number of joules of electrical energy race into the resistor and get converted to heat.

The above equation isn't used very often. Instead, we usually think in terms of charge flow and energy flow, not in terms of hunks of charge or hunks of energy which move. However, thinking in terms of charge hunks or energy hunks makes the concepts sensible. Once you grasp the "hunks" concepts, once you know that energy is needed to push each hunk of charge against a voltage force, afterwards we can rewrite things in terms of amps and watts. Afterwards we can say that it takes a FLOW of energy (in watts) to push a FLOW of charge (in amps) against a voltage. Yet first it's important to understand the stuff that flows. Think in terms of coulombs of charge and joules of energy.

The charge-flow and the energy-flow are usually written as amps and watts. This conceals the fact that some quantities of "stuff" are flowing. But once we understand what's really going on inside a circuit, it's simpler to write amperes of charge-flow and watts of energy-flow:

```
VOLTS x COULOMBS/SEC = JOULES/SEC   It takes a flow of energy to make
charge flow forward against pressure
```
Don't forget that "Amps" is shorthand for the charge inside wires flowing per second. And "watts" is shorthand for flowing energy. We can rewrite the equation to make it look simpler. It's not really simpler. We've just hidden the complexity of the above equation. It's shorthand. But before using the shorthand, you'd better understand the full-blown concept!
```
VOLTS x AMPERES = WATTS         Pushing a current through a voltage
requires energy flow or "power."
```
We can get the Ohms into the act too. Just combine this equation with Ohm's law. Charge flow is caused by volts pushing against ohms, so let's get rid of amps in the above equation and replace it with voltage and ohms. This forms the equation below. Notice: increasing the voltage will increase the energy flow that's required, but it also increases the charge flow... which increases the energy flow too! If voltage doubles, current doubles, and wattage doesn't just double, instead the doubling doubles too (wattage goes up by four times.) Tripling the voltage makes the wattage go up by NINE times. Write it like this:
```
VOLTS x (VOLTS/OHMS) = WATTS    Voltage applied across ohms uses up a
constant flow of electrical energy
```
So, if you double the voltage, energy flow increases by four, but if you cut the friction in half while keeping voltage the same, energy flow goes up by two, not four. (The amperes also change, but they're hidden.)

Here's one final equation. It's almost the same as the one above, but voltage is hidden rather than ampereage:

```
(AMPERESxOHMS) x AMPERES = WATTS  When charge is flowing against ohms,
electrical energy is being used up
```
So, the watts of energy flow will go up by four if you double the current. But if you can somehow force the current to stay the same, then when you double the friction in the circuit, the energy flow will only double (and the voltage will change, but that part's hidden.)

And finally, here are a couple of things which can mess you up. Think about flowing power. Try to visualize it. I hope you fail! Remember... POWER DOESN'T FLOW! The word "power" means "flow of energy." It's OK to imagine that invisible hunks of electrical energy are flowing across a circuit. That's sensible. Electrical energy is like a stuff; it can flow along, but "energy flow" cannot flow. Power is just flowing energy, so "power" itself never flows. Beware, sincemany people (and even textbooks) will talk about "flows of power." They are wrong. They should be talking about flows of electrical energy. "Flow of power" is a wrong (and fundamentally stupid) concept.

OK, I've run out of steam for now. Ooo! Ooo! No I haven't. I must now go on a crusade about How Capacitors Are Explained Wrong. Then I'll go on and on about Why most explanations of transistors basically suck.

```
Created and maintained by Bill Beaty. Mail me at: .