We've all heard of voltage and “high voltage”; fewer people are familiar with current and resistance but these are the fundamental characteristics of a circuit. Every electrician, and everybody who works on or services appliances, or electronics knows about these things. And, by the way, if you want to get your ham radio license, this theory is needed for the license if you really want to understand things.

Voltage, or potential, is a force available that causes electrons to move. The current is the amount of electrons that flow past a point in a given time. The unit of current, the Ampere, or simply “Amp”, is a set number of electrons flowing past a point in one second. (The number is one coulomb per second, and a coulomb of charge is 6.241×10^18 electrons. That scientific notation number is 6.241 quintillion, 6,241,000,000,000,000,000, a number even larger than the rolled up value of all the CDOs and other imaginary assets the banking system generated before the '08 crash. But not by much, only by a factor of about 1000. You will never need to know this, it's just a fun number.)

The most fundamental relationship in all of electricity and electronics is Ohm's law, which combines voltage and current with a new property called resistance. Resistance (R) is opposition to current flow, and is the voltage (V) in a circuit divided by the current (I) going through it. I find formulas with multiplication easier to remember than division so I remember it as

V=I*R

which says that the voltage change across a resistor is the current times the resistance. The units of resistance are ohms, like the law; I've already talked about volts and amps, the units for the other two. Ohms are often indicated by the Greek symbol omega, which this editor doesn't even have a symbol for. If you search online for help on Ohm's law you will find much of it refers to Voltage as E – for electromotive force. This is an old term that seems to only be used by beginners, but since beginners are the folks who will look for the explanations, that's the term a lot of the web sites use.

While we think of high voltage as dangerous (and it is...) the reason is that a higher voltage can force a larger current through a resistor (like you, for instance). How much current is dangerous? As little as .06 Amp (60 milliamps) of AC at the power line frequency can kill if it goes through the heart. For DC, the number is somewhat higher, about 300 to 500 mA, if current passes through the heart to complete the circuit. You can see that if you work on electrical systems, and your body represents some fixed resistance, a 440V system (say) will generate higher currents than a 12V system. I have heard tales of as little as 20 mA and 32V being fatal and I know everyone at my company who works on anything above 50V requires special electrical safety training.

A very common illustration is a water tank and pipe. The tank applies pressure, the potential, and the size of the pipe limits how much water can flow. That's the current. The size of the pipe that limits the amount of current the tank can deliver is the resistance.

The power (stated in Watts) in a DC circuit is simply voltage times current in amps:

P=V*I

Since voltage and current can be expressed in terms of resistance, you can substitute those equations into this one and get power dissipated in a resistor, expressed as the current in the resistor or the voltage across it. Your "power company" doesn't really sell you power, they sell you energy. The metric unit for energy is a Joule, and a Watt is a Joule/second ( "Watt's a Joule per second? Yes!") so a Joule is a Watt*Second and the power company sells you multiples of that, usually kilowatt hours (1000 watts for a 3600 seconds).

Confusing? You'll find many, many versions of this chart online, which gives you a group of formulas to use, without doing the multiplication on paper or in your head (this one from http://www.radioelectronicschool.net/index.php?cmd=supplementary ) :

So what happens if you have more than one resistor in a circuit? That depends on how they're connected. If they are in series, “end to end”, the current has to go through them all one after another, and the total resistance simply adds them up:

Rtotal = R1 + R2 +R3+...
In this circuit, the two 10 ohm resistors would add up to 20 ohms. The left side of “R1” has the battery positive voltage connected to it, and the right side of “R2” has zero on it – it's connected to the negative terminal. The only unknown voltage is the one in the middle of the two resistors, and with equal resistors, it's half the applied voltage. We'll talk about voltage dividers in another post.

If the resistors are in parallel, the current divides between them proportional to the size of the resistors. They add in a peculiar way, as the reciprocal of reciprocals:

Rtotal =1/(1/R1+1/R2+1/R3+...)

In the special case where there are two resistors:

1/(1/R1+1/R2) = (R1*R2)/(R1+R2)

With a modern scientific calculator, you might find either one just as easy to enter, and remembering only one form will help. I tend to use the reciprocal of reciprocals form because I tend to do this for several resistors more often than just two.

The easiest case is two identical resistors, and here the total works out to be ½ of the resistor value. It is always true (and worth remembering) that the resistance in a group of parallel resistors is always smaller than the smallest resistor in the combination.

In the parallel circuit, both resistors have the same voltage across them – they're both across the same battery, after all – but the current through them varies with the smaller resistor getting the higher current. If these were a 10 and 5 ohm resistor, the current in the smaller one would be twice the current in the bigger. Also, since it's now a smaller load (the two in parallel are 3 1/3 ohms instead of 5) the total current is higher than the current into two 10 W resistors.

There are some other things to see in the example circuits. Voltage is always measured across something: for example, the battery has a positive and negative lead and the voltmeter leads go one to each side. I could put one lead on the junction of the two series resistors and the other lead on the other end of either resistor and measure the voltage across it; one direction will be positive voltage, the other negative (if I don't move the probe on the center). Current always goes through something; I can't measure the current in R1, for example, without opening the wire between the resistor and either the top or bottom of the voltage source. So voltage is always measured in parallel, while a current is always measured in series. There's an exception to the breaking the wire thing: there are meters that clamp on and measure current by the magnetism it produces (yes, all electric current causes a magnetic field – it's the law).

OK, so why is this worth knowing? In a circuit like our solar panel project, all of the losses add up like resistors. If we have a wire with some amount of loss, we can cut the loss in half by running an identical wire in parallel with it (which is the same as doubling the cross sectional area of the wire). If we add connectors, or other pieces of wire in series with the panel terminals, we've added series resistances and the total loss goes up.

If you take an electrical engineering circuits class, you'll get a lot more information, like Ohms' first name (Joe Bob), Ampere's first name (also Joe Bob), and other trivia, but not much more content. You'll solve a billion and six problems with different connection configurations – some of which are useful for concepts introduced later in the curriculum, but this is the meat of DC circuits.

(Strangely, everyone in the history of electricity was named Joe Bob).

Readers: I need feedback on wether or not this is any good. I glossed over a lot of material that people might not be comfortable with: SI prefixes like kilo, milli and such; what those squiggly things are, the whole "what's a schematic diagram" thing. Discomfort with Math. That sort of thing. I need feedback on how much more detail I need to add.

If the resistors are in parallel, the current divides between them proportional to the size of the resistors. They add in a peculiar way, as the reciprocal of reciprocals:

Rtotal =1/(1/R1+1/R2+1/R3+...)

In the special case where there are two resistors:

1/(1/R1+1/R2) = (R1*R2)/(R1+R2)

With a modern scientific calculator, you might find either one just as easy to enter, and remembering only one form will help. I tend to use the reciprocal of reciprocals form because I tend to do this for several resistors more often than just two.

The easiest case is two identical resistors, and here the total works out to be ½ of the resistor value. It is always true (and worth remembering) that the resistance in a group of parallel resistors is always smaller than the smallest resistor in the combination.

In the parallel circuit, both resistors have the same voltage across them – they're both across the same battery, after all – but the current through them varies with the smaller resistor getting the higher current. If these were a 10 and 5 ohm resistor, the current in the smaller one would be twice the current in the bigger. Also, since it's now a smaller load (the two in parallel are 3 1/3 ohms instead of 5) the total current is higher than the current into two 10 W resistors.

There are some other things to see in the example circuits. Voltage is always measured across something: for example, the battery has a positive and negative lead and the voltmeter leads go one to each side. I could put one lead on the junction of the two series resistors and the other lead on the other end of either resistor and measure the voltage across it; one direction will be positive voltage, the other negative (if I don't move the probe on the center). Current always goes through something; I can't measure the current in R1, for example, without opening the wire between the resistor and either the top or bottom of the voltage source. So voltage is always measured in parallel, while a current is always measured in series. There's an exception to the breaking the wire thing: there are meters that clamp on and measure current by the magnetism it produces (yes, all electric current causes a magnetic field – it's the law).

OK, so why is this worth knowing? In a circuit like our solar panel project, all of the losses add up like resistors. If we have a wire with some amount of loss, we can cut the loss in half by running an identical wire in parallel with it (which is the same as doubling the cross sectional area of the wire). If we add connectors, or other pieces of wire in series with the panel terminals, we've added series resistances and the total loss goes up.

If you take an electrical engineering circuits class, you'll get a lot more information, like Ohms' first name (Joe Bob), Ampere's first name (also Joe Bob), and other trivia, but not much more content. You'll solve a billion and six problems with different connection configurations – some of which are useful for concepts introduced later in the curriculum, but this is the meat of DC circuits.

(Strangely, everyone in the history of electricity was named Joe Bob).

Readers: I need feedback on wether or not this is any good. I glossed over a lot of material that people might not be comfortable with: SI prefixes like kilo, milli and such; what those squiggly things are, the whole "what's a schematic diagram" thing. Discomfort with Math. That sort of thing. I need feedback on how much more detail I need to add.

## 16 comments:

"Joe Bob" - snerk.

You're going to make me did my EE101 book out of the attic ...

It's truly one of the great mysteries of the world that all those French, Italian, and other European guys were named Joe Bob...

"I need feedback on wether or not this is any good"

I'm not sure that you intended to question regarding a castrated goat (wether)??

However. whether you need more detail regarding electrical theory depends I suppose on how far and what direction you want to take this...

As basic info though - very good summary. Somehow that reciprocal of the sum of reciprocals cracks me up. Strange that way I suppose.

This looks good so far, SGB, but I have a hard time judging since it's all review for me so far. I'm looking forward to your next articles.

Lacks the homeyness of a Joe Bob Mims III notebook, but it's quite readable.

Volt-aire's first name was Jimbo, but that's cuz he was a philosopher, not an electrician.

Looks pretty good to me so far, SG, and you didn't talk about hoses even once.

The whole reciprocal thing did cause me some discomfort, but I put some ointment on it.

Less technicality, more practicality.

God as is, to the novice's eye. You are laying a foundation for subsequent use (and review, if needed).

-- CA

Make that "good".

-- CA

Far more interesting than my first circuits class. But don't forget the part about the magic smoke that makes it all work!

I've also observed that another important force in the world of electricity (in addition to electromotive force)is alcohol. Its amazing what an engineer can accomplish for the reward of beer! (Only the good stuff though, Natty Light won't make it happen)

Anon 6:38 - This technicality

isthe practical. As the title states it is the least you should know in order to be able achieve any practical result.He will move on to show you why and how in later installments.

Let me try to make an analogy: In order to hit a target with a projectile you must know something about gravity. In the simple case of a baseball this knowledge can be acquired "intuitively" by repeated experiments. If, however, you wish to lob a shell 50 miles and hit the target intuition will not do. You need to do calculations. Even at the extremes of visual range the sniper cannot work without his spotter working the calculations.

Unlike a baseball we cannot measure electric currents with our eyes and muscles. Even at the "shortest range" we must apply measurements with tools and make calculations to achieve any intuitive sense of what is going on.

Otherwise you're just "pitching" blind. With projectiles that can blow up and start house fires.

You are being offered the gift of electrical sight.

It's time for me to take a break from work when I can recognize the tool you're using by a picture of a simple circuit diagram...

Q

That may be another topic for another day, but it's the best schematic tool I've got at home.

@kfg

Thank you for dumbing it down for me. More practical, please.

"Thank you . . ."

You're welcome.

It's a good one ... better than even some pros suspect.

Can't beat the price either

Q

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