Physical Laws: Volts, Amps, Coulombs, Joules, Watts

CS 641 Lecture, Dr. Lawlor

Physical reality places surprisingly pressing limitations on modern computer performance.

One Watt is a Joule per second (W=J/s). For example, the Fukishima Daichi nuclear plant was rated at 4.7 gigawatts, and could power a medium-sized city, but the cooling system is absolutely life critical. My ordinary 140hp four cylinder passenger car produces over 100,000 watts, and needs a dedicated liquid cooling system to keep from melting down. My big desktop replacement laptop burns 80W at idle, and over 130W when the graphics card is cranking, so can get by with a copper finned heatsink and dedicated fan. A cellphone might burn 2W at maximum usage, so needs no fan. A single LED burns a few milliwatts. Generally:

Anything over a megawatt needs a dedicated liquid cooling *tower*.
Anything over a kilowatt needs dedicated liquid cooling, like a radiator. Ordinary personal computers haven't hit this point yet, although supercomputers and data centers have been liquid cooled since the Cray-2 in 1985.
Air cooling with a heatsink works well between a few dozen and a few hundred watts. This is the thermal regime of most modern PCs.
Air cooling without a heatsink is fine below a dozen or so watts. This is the design range of most cellphone and some portable processors.

One amp is a coulomb of electrons (6.24x10¹⁸ e^-) per second. Typical microcontroller signals are milliamps, typical wall plug currents are up to a few dozen amps, and typical arc welding current is about a hundred amps.

In order of delivered amps at 12 volts:

A small battery like a garage door opener battery puts out less than 1 amp, and not for very long either.
A PC power supply typically delivers 10-25A on the yellow +12V line.

To power up a PC power supply without the motherboard, just ground the green wire. I use a paperclip for this.
The 5V and 3.3V have somewhat higher amp ratings, but usually less total power delivered (due to the lower voltage). Thus, most high end graphics cards and CPUs mostly draw 12V power as the input to their core voltage DC-DC converters.
To reduce fire hazard, a PC power supply will turn itself off ("crowbar") if you draw too many amps. To reset the PC power supply, just wait; if impatient, you can unplug the power supply and ground the AC input pins (this discharges some internal capacitor).

A car's lead-acid battery will deliver hundreds, or even thousands of amps at 12V. Unlike a PC power supply, you can burn the plastic insulation from thin wires with even a momentary short, and can rapidly melt metal.

An electrical arc is actually a fairly useful component:

An arc consists of ionized gas at thousands of degrees, and glows extremely brightly. Carbon arc lamps were used for indoor and auto illumination in the late 1800's, but operation is finicky (striking the arc is tricky) and bulb life is short ("up to" 100 hours).
The energy in an arc can be used to melt metals for welding, called arc welding. Common stick, MIG, and TIG are all forms of arc welding.
Sadly, nothing about arc is safe: it moves unpredictably with the wind, convection, or magnetic fields, it can burn your skin, the UV can burn your eyes, and it's conductive to electricity. However, arc is beautiful!

A surprising variety of electrical components can be constructed from ordinary wire:

Put enough amps through a wire, and it will get hot enough to glow.

Keep the wire in a vacuum, and make the wire from tungsten so it won't melt, and you have a light bulb.
Put a thin wire in a glass tube, and you have a fuse (burns and opens the circuit if the amp draw is too high).
Coat a thin wire in pyrotechnic material, and you have an electric match (used to set off fireworks remotely, under computer control).

It takes some electrical energy to push current through a wire. The longer the wire, the more resistance (an entire 500 foot spool of thin 20ga doorbell wire reads about 5 ohms). High power resistors are still "wire wound", the active components made from 100% wire! Low power resistors are usually a thin film of carbon.
Moving electrons induce a magnetic field around a wire. With enough electrons, or fields wrapped in the same direction so the field is reinforced, you have an electromagnet.

The field gets stronger when you add a ferromagnetic core in the middle of the coil.
Huge electromagnets are used for picking up and moving large pieces of iron, including difficult to pick up scrap.
An inductor stores electrical energy in the magnetic field of a coil, which smooths out current flow.
An electromagnetic coil that moves a switch is called a "relay". In the 1940's and early 1950's, most computers were built using relays as the switching element. Relays are slow (a few hundred hertz, tops) but strong (10A ratings are common) and reliable (against EMP, electrostatic shock, hooking the batteries up backwards, being dunked underwater, ...).
The magnetic field from an electromagnet can be used to move objects, making a linear or rotating motor in a huge variety of ways. We used the Lorentz force to spin a tiny neodymium magnet, which at 12V spits off big showers of sparks.
Electromagnets also "work backwards" as generators, turning changing magnetic fields into electrical current.

A 1 ohm resistor will conduct no more than 1 amp of current at 1 volt. Ohm's law (V=I R or volts = amps * ohms) is more of a guideline, an assumption of linearity that is only valid for resistive materials (OK for most metals, poor for most insulators, liquids, or semiconductors).

Power law: P = I V, or watts = volts * amps. A 0.1 ohm piece of wire will drop 1 volt if you push 10 amps through it, which takes 10 watts: the wire might get fairly warm, but will still be there. The same wire taking 100 amps will drop 10 volts, so must dissipate 1000 watts: the wire is going to feel some serious heat.

For example, a current-signaling network might represent individual byte values as groups of 0 to 255 electrons. 255 electrons per sample at 100 million samples per second is 25.5x10⁹ Ge^-/s. One Coulomb is 6.24x10¹⁸ e^-, so that's a current of 4x10^-9 C/s, or 4 nano-amps. At 1V signal strength, a one-ohm wire will lose 4 nano-volts. Not much! Of course, in practice we usually use voltage-signaled networks, and single electrons have a bad habit of obeying only the funky quantum laws instead of ordinary classical dynamics, which makes things much more complicated.