Computing stuff tied to the physical world

Easy Electrons – Resistors

In Hardware on Dec 12, 2010 at 00:01

A few days ago, I was completely overwhelmed by the positive response to a couple of posts about electronics principles such as power and circuit diagrams. Since I love to share what I’ve learned (and still learn) about this world full of discoveries, inventions, and creative engineering, I’ve been thinking about how to fold such a topic into this daily weblog.

The result is Easy Electrons – a series which will cover various aspects of electronics from the viewpoint of a technology enthusiast with a non-electronics background.

I’ve got some ideas about the frequency and topics for these posts, but I’m not commiting to a schedule or specific subjects just yet. Let’s see how it goes, and let me know what you think of these posts. Your comments will help guide me.

With that out of the way – let’s have some fun with electronics, eh?

But ya’ can’t run before you walk. This kick-off post has to go into some basic stuff. You may well know all this, but if in doubt, make sure you “get it”. Without these preliminaries, you will not be able to make sense of everything else in the upcoming posts of this series.

Resistance is not futile!

IMO, there is no concept more important in electrical circuits than resistance. One reason is that it’s everywhere, even the thickest copper wire has some resistance, however small. And an insulator, i.e. the stuff that prevents electricity from flowing all over the place, has essentially infinite resistance.

Take a voltage (or, using the water analogy: lift some water up). Once you let it “go”, it’ll want to flow. It does this using the path of least resistance. Thick solid copper pipe: huge current, massive power surge. Very thin wire: tiny current, squeezing its way through and heating up the wire. If the squeeze is strong enough (enough voltage) the wire will heat up to the point where Thomas Alva Edison made an incandescent light!

Voltage wants to flow. And when it does, it creates a current. It flows quickly when the resistance is low, it flows more slowly when the resistance is high, and it fails to flow when the resistance is infinite. That’s also why electricity will always pick a copper wire over plain air.

It’s time to introduce Ohm’s law:

    E = I x R

In words: voltage = current times resistance.

Voltage is described in volts (thanks to Alessandro Volta), current is described in amps (courtesy André-Marie Ampère), and resistance is described in ohm (due to Georg Simon Ohm).

I’ll simplify the world by saying: in simple cicuits with no effects from electric and magnetic fields, Ohm’s law is all you need to know. If you know any two of the quantities, you can calculate the third.

I won’t go into them now, but if you also learn the two Kirchoff’s circuit laws, then you’ll have some incredibly powerful tools to explain what’s going on, even in circuits with dozens of components, connected in all sorts of funky ways.

Physicists and chemists will be used to this, but if you come from the world of software, then note that these laws are really quite amazing: they let you predict what will happen when you hook up a circuit. Laws such as this were not “created” to terrorize kids in school, they are really extremely useful!

Let’s try it:

Screen Shot 2010 12 05 at 15.16.27

What’s the voltage on the right side? (assuming no load current)

I’m going to skip several details, but here’s how I would reason about it:

  • we want to know the voltage over the lower resistor
  • we know its resistance, so if we knew how much current is flowing, we could calculate it
  • the current flows through both resistors
  • the current IN is the same as the current OUT
  • so the same current flows through both resistors
  • we know the voltage over the total
  • if we knew the total resistance, we could derive the current through both
  • once we do, we know the current through the lower resistor
  • and from there, we can calculate the voltage, as requested

Question: what is the resistance of two resistors placed in series, one after the other?

Answer: this is one of those facts you’ll just have to memorize – resistance of R1 and R2 in series = R1 + R2.

  • so we have 9 volts over 3 kilo-ohm, i.e. 3000 ohm
  • the current is 9 / 3000 = 0.003 amps, i.e. 3 milliamps
  • voltage over 1 kΩ is 1000 x 0.003 = 3 volt

So the final answer is 3 volts.

But don’t stop there, please:

  • What if we use a 3V battery? Answer: (3/3000)*1000 = 1V.
  • How about a 12V power supply? Answer: (12/3000)*1000 = 4V.
  • See the pattern?

The two resistors act as a voltage divider. They don’t really “care” about the input voltage, they will simply divide it by 3. Because the ratio of the total to the lower resistance is (2+1)/1 = 3. This is also the reason why I drew that schematic in this particular way: it illustrates the voltage “drop”.

Hold on to that insight. Electric circuits usually have lots of voltage dividers. Whenever I see resistors in series, I try to determine what voltage is placed over them. And sure enough, most of the time, that’s what the resistors are used for. It works for any voltage. It also works for varying voltages: if you have an audio signal in the form a a rapidly varying voltage, then the voltage divider will simply pass the signal through, at a reduced voltage level.

Not every resistor is used as voltage divider. But more often than not, that’s all they do when used in series.

Easy Electrons!

P.S. Would you believe that I found out about this tutorial after writing the above? Heh… synchronicity :)

  1. Just to be pedantic… these calculations are precisely true only in the case that no current flows out the wire to the right (Vout), that is, infinite load resistance. A typical digital multimeter has an internal resistance of 10 Mohm. So if you measure Vout with your DMM, that 10M is in parallel with the lower resistor. For this example (R=1k), that’s only a 0.01% change, but it’s significant if you have much larger value resistors.

  2. Nice article, but be careful about easy electrons, the tricky little so and so’s go the wrong way ;-)

  3. You should write a book called “Easy Electrons” and publish it! I’m currently learning my son to play with LEDs, resistors and batteries (his name for resistors is “voltage absorbers”) and even at this level it can sometimes be quite difficult to explain the smallest, trivial things. So far, I think I got it :-)

  4. For those noobs out there you could include also some calculations on how having a load current influences this ;) Looking forward for your power supply tutorial, or even better, LiPo+solarcell battery pack for JeeNode :)

  5. Yeah, I had a Jeelabs syncronicity experience too recently. End of november I bumped into this DNS resolve issue. During the weekend I read RFC 1034/1035 to see if I could find a solution. The next monday I read the Jeelabs post about the patch of this issue by Gerard Chevalier…

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