SHORT VERSION: HOW ARE WATTS, OHMS, AMPS, AND VOLTS RELATED?
2000 W. Beaty BSEE

Oooo, good question. Some info is at ELECTRICITY FAQ, also Electricity is not energy and Electricity Misconceptions. But none of these have a direct answer to your question. A useful answer is going to be HUGE. Be warned! (grin)

Here's the extremely short answer. Voltage pushes charges through an object which has electrical resistance, and this heats up the resistive object. The flow of the charges is measured in amperes, the flow of electrical energy and heat output is measured in watts, and the resistance is measured in ohms.

First the watts and amperes. These are somewhat confusing because they are the names of flows, but we never talk about the STUFF that flows. Electric current isn't a stuff, electric current is the flow of a stuff. What is the name of the stuff? Charge.

AMPERES

• Charges
• Electrons
• "Charge-stuff"

A quantity of charge is measured in units called COULOMBS, and the word "ampere" means the same thing as "coulomb of charge flowing per second." Why do I say that amperes are confusing? Well, suppose we had no name for water, yet our teachers wanted us to learn about "fluid flow". Suppose we all had to learn about "gallons-per-second," but without knowing anything about gallons, or about water, or about the very idea of "liquids." If you'd never learned the word "gallon", and if you had no idea that water even existed, how could you understand "currents?" That's the problem with electricity and amperes.

We can only understand the flow (the amperes) if we first understand the stuff that flows in wires: the charge, the coulombs.

CHARGE

"Charge" is the stuff inside wires, but usually nobody tells us that ALL METALS are full of charge. Always. A hunk of metal is like a tank full of water, and the "water" is the movable electric charge inside it. In physics classes we call this "the electron sea" or even "electric fluid." This charge is part of all metals. In copper, the electric fluid is the outer electrons of all the copper-atoms.

The movable charge-stuff within metals gives them their silvery color. We could even say that charge-stuff is like a silver liquid (at least it's silvery when it's inside metals.)

Note that this charge is "uncharged", it is neutral. Is this impossible? No. The charge inside of metals is neutral because each electron has a corresponding proton nearby, and the fields from the opposite charges cancel out. The charge is cancelled, but this doesn't mean that the charge-stuff is gone! Even though the charge inside a metal is cancelled out, we can still force it to flow along. We can make the metals own electrons flow past its protons.

ELECTRIC CURRENT

When the charge-stuff within metals is forced to flow, electric currents are created. We measure the currents in terms of amperes. The faster the charge-stuff moves, the higher the amperage. Also, the MORE charge-stuff that flows (through a bigger wire) the higher the amperage. A fast flow of charge through a narrow wire can be the same current as a slow flow of charge through a bigger one.

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

Generators are magnet-driven charge pumps. The moving magnetic fields push the wire's charges, creating the amperes, but this only occurs when a complete circuit is present. Break the ring and you create a blockage, since the charges can't easily jump across the break in the ring. A complete ring is a simple electric circuit. Cut the ring and install a battery in the cut, and the battery can pump the ring's charge-stuff in a circle. Make another cut, install a light bulb, and the "friction" of the narrow filament against the flowing charge-stuff creates high temperatures, and the wire filament inside the bulb glows white-hot.

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

WATTS

What is power? The word "power" means "energy flow." It might help you to avoid thinking about "power" at the start. If you first practice thinking in terms of energy flow instead of power, and joules per second instead of watts, eventually you'll gain a good understanding. Once you know what you're talking about, then 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 begin by saying "power" and "watts", you might never really learn what these things are, because you never really learned about energy flow.

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 is composed of magnetic fields and electrostatic fields. A joule of radio waves is the same as a joule of electrical energy. What does this have to do with understanding electric circuits? Quite a bit! But I'll come back to this later.

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 injects joules of energy into the ring, and the light bulb takes them out again. Joules of energy flow between the battery and the bulb. They flow 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 IMMEDIATELY. There will still be some joules moving along the wires, so the bulb will stay on for a tiny fraction of a second, until all the energy arrives. Remove the battery, and the light bulb goes dark ALMOST instantly.

AMPERES ARE NOT A FLOW OF ENERGY

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 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. The electrical ENERGY flows in the space around the wires, while the electric CURRENT 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". You've probably heard that voltage is like electrical pressure. What's usually not taught is that voltage is part of static electricity. If I grab electrons 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 extending across the space between them. THIS FIELD IS THE VOLTAGE. Electrostatic fields are measured in terms of volts/distance, and if you have a field, you always have a voltage. To create voltage, take charges out of one object and stick them in another.

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. This 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. And finally, it caused the charge-stuff inside the light bulb filament to begin flowing. 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. 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 charge to flow through the light bulb filament. But where does energy fit into this? To understand that, we have to know about electrical friction or "resistance" to.

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. (This happens whether the water is flowing or not.) 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 of the thin wire to start moving. Double the length of the wire, and you double the friction. The extra cuts the charge flow (the amperes) in half. THE FRICTION IS THE "OHMS", IT IS THE ELECTRICAL RESISTANCE. To change the charge-flow, we can change the resistance of our pice of wire by changing its length. 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 wire ends. Which doubles the flow. We've just discovered "Ohm's Law", which says that the flow is directly proportional to the pressure difference, and if the pressure goes up, the flow goes up in proportion. It also ways that if the resistance goes up, the flow goes DOWN by a 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 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 charges flow around the circle, and also sends energy to the light bulb. It takes voltage to force the charges to flow, 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. This is called "Ohm's Law", and we can write it like this:

VOLTS/OHMS = COULOMBS/SEC

It says that a large voltage causes coulombs of charge to flow faster through the wire. But we usually think of current in terms of amps, not in terms of flowing charge. Here's the common way to write Ohm's law:

VOLTS/OHMS = AMPERES

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 too: THE MORE FRICTION YOU HAVE, THE SLOWER THE FLOW. If you keep the voltage the same (in other words, 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 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.

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

The more current, the more volts you get. Or, if the current is forced to stay the same and you increase the friction, 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 know the voltage, and we want to find the amperage. However, transistor circuits involve constant currents, so the above ideas are very useful.

But what about watts? When charge is being pushed through an electrical resistance, electrical energy is lost and heat is created. A certain amount of energy is flowing into the resistor device every second. If we increase the voltage, more energy flows into the resistor and gets converted to heat. If we increase the flow of charge, same thing: more heat flows out per second. Here's how to write this:

VOLTS x COULOMBS/SECOND = JOULES/SECOND

For every coulomb of charge that's driven through the resistor, a certain number of joules of electrical energy flow into the resistor and they flow out as heat.

The charge flow and the energy flow are usually written as amps and watts. This conceals the fact that quantities of "stuff" are flowing. But once you understand what's really going on inside a circuit, it's simpler to write amperes of charge flow and watts of energy flow. IF WE INCREASE THE VOLTAGE, THE CHARGE FLOW INCREASES, AND THE ENERGY FLOW INCREASES EVEN MORE. Doubling the voltage-pressure caus

VOLTS x AMPERES = WATTS

We can get the Ohms into the act too. Just combine this equation with Ohm's law. If you increase the voltage, it increases the flow of charge through the electrical friction device. But since voltage AND current both get larger at the same time, the energy flow increases even more. If voltage doubles, current doubles, and wattage doesn't just double, instead the doubling doubles too (wattage goes up by four.) Write it like this:

VOLTS x VOLTS / OHMS = WATTS

So, if you double the voltage, energy flow increases by four, but if you double the friction while keeping voltage the same, energy flow gets cut in half (not in 1/4.) The amperes change too, but they're hidden. Here's one final equation. It's the same as the one above, but voltage is hidden rather than ampereage:

AMPERES x AMPERES x OHMS = WATTS

So, the watts of energy flow will go up by four if you double the current. But if somehow you can force the current to stay the same, then when you double the friction the energy flow will double (and the voltage will change.)