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.
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.
- 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
In order of delivered amps at 12 volts:
An electrical arc is actually a fairly useful component:
- 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.
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).
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
A surprising variety of electrical components can be constructed from ordinary wire:
- 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!
- 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
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
- 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
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.