By Mike Rivers
We use common electrical terminology in our everyday life—a flashlight battery is one and a half volts, the monitor amplifier is 150 watts per channel, and the speakers are 8 ohms. A few months back, while discussing some articles with Our Friendly Editor, I heard him say, “Maybe our readers would like to know what a volt really is.” Well, here’s the scoop.
Electricity is all about storing and moving electrical charges. The basic unit of charge is the coulomb (pronounced “cool ohm”), a quantity of 6.24 x 1018 (six billion billion) charge carriers (usually electrons). That’s a lot, and no, we don’t expect you to count them all! The more coulombs stored in one place, the greater the voltage. The more electrical charges that move from one point to another in a given period of time, the greater the electrical current.
Water is often used as an analogy to explain electricity, and it’s a fairly good one. The amount of water in a bucket is analogous to voltage. Punch a hole in the side of the bucket and water will run out. The water flowing out of the hole is analogous to the flow of electrical current.
The size of the hole is analogous to electrical resistance. The larger the hole, the faster the water will flow, the smaller the hole, the slower the flow. Just like resistance to water flow, for a given voltage, a lower resistance will result in greater current flow, a greater resistance will restrict the amount of current that can flow in a circuit. We’ll talk more about this relationship below.
For a bucket of a given diameter, the more water we put in it, the higher the water level will be, and therefore a greater amount of pressure will be available to push water out the hole that we punch near the bottom. While the size of the hole limits the number of ounces per second coming out, the pressure of the water as it comes out of the hole is a function of the height of the water in the bucket. The water will spurt out furthest when the bucket is full. As the water level in the bucket drops, the pressure drops, causing the water (which is still flowing at the same rate) to not go as far horizontally before gravity pulls it down. Applying our analogy, the more charge we have in storage, the higher the voltage available. And as the charge drains off, the voltage drops. (See the pictures)
Scientists had correctly theorized that lightning was a result of electrical charges stored in the atmosphere finding their way “out of the bucket” and flowing down to earth. Benjamin Franklin attempted to prove the relationship between charge and electricity with his famous kite experiment. Folklore tells us that about 250 years ago he captured electricity by flying a kite during a lightning storm and allowing electric charge from the lightning to flow down the wet kite string, to a metal key, and into a Leyden Jar, a device (a capacitor, really) for storing electrical charge.
There’s no clear evidence that he actually performed the experiment as it is usually described—the best evidence that he didn’t is that he remained alive to continue to study and write about electricity. He did, however, conduct several well-documented experiments using lightning as his source of electrical charge. Franklin was aware of the dangers of working with lightning. Don’t try this at home!
The bottom line was that Franklin was able to carry a jar of electrical charge from the storm into his laboratory and perform further experiments, the first of which was probably to connect it to an instrument called an electroscope to verify that there actually was some electrical charge stored in the jar.
Franklin wasn’t the only one studying electricity in the eighteenth century—credit must go also to French and Italian scientists André Ampère and Alessandro Volta (honored respectively by the subject of this article, amps and volts). Being a publisher and politician as well as a scientist, Franklin managed to get his name into all the history and science books as the important contributor that he was.
What can you do with a jar of electrical charge? Well, really not a whole lot. You can count how many coulombs you have in the jar and express the voltage that way, but a more practical way to measure voltage, and the way we always do it in electricity and electronics, is to measure the potential difference between two terminals of our voltage source.
Back in the water
Going back to our water analogy for a moment, let’s fill up the bucket, but this time punch two holes in it, one near the top and the other near the bottom. Since the pressure behind each stream (assuming the holes are the same size) is a function of the weight of the water above the hole, the distance that each stream spurts horizontally is a function of gravity, which is in turn a function of the absolute distance of the bucket from the center of the earth.
The stream coming out of the top hole has less water above it so it will come out at a lower pressure than the stream at the bottom. While we don’t know the exact height above the center of the earth of each hole, we know the difference in their heights, and can therefore express the pressure difference. The difference in distance that each stream travels horizontally is analogous to the voltage difference between two terminals on our voltage source.
A practical battery has two terminals, each of which is at a different absolute electrical potential. We may not be able to express what the absolute potential of each terminal is because we don’t know the reference point, but we can easily measure the potential difference between the two terminals, and that’s what we call the voltage.
So much for volts for the time being. Electrical current, measured in amperes (sometimes shortened to amps) is what you get when those charge carriers flow from one place to another. A current of one ampere is defined as the movement of one coulomb’s worth of charge past a given point in one second. That’s a whole lot of electrons, but remember, one electron is very small.
Returning to our bucket-of-water analogy for a moment, for a given amount of water (voltage), the cross sectional area of the hole determines the amount of current that will flow. A large hole dumps out a large volume of water in a given amount of time, while a smaller hole will allow a smaller volume of water to flow out of the bucket.
And as we pointed out above, since the size of the hole in the bucket limits how much water at a given pressure can flow out, the hole is analogous to the third important parameter in basic electricity: resistance. The larger the hole, the less resistance it presents to water flow, so, for a given water pressure, more water (hence more current) can flow.
In order for current to flow, you need a complete circuit (which comes from the same word as “circle”), a path through which a voltage source can push a current. A circuit is an interconnection of actual physical real-world components. A component is a part of a circuit that has two terminals to which connections can be made. A junction is formed when two or more components are connected.
In the real world, voltage and current always go hand in hand. You can’t have one without the other except in abstract theory where it’s assumed that you have no resistance. The fundamental relationship between voltage, current, and resistance in a circuit was described by the German physicist Georg Ohm. In fact, this relationship is so fundamental that it became a law, Ohm’s Law, known by rote by just about everyone who has learned anything about electricity. (Dr. Ohm also lent his name to our unit of resistance, the ohm, abbreviated Ω.)
In words, Ohm’s law states that the current in a circuit is directly proportional to voltage and inversely proportional to resistance. You probably know it as I=V/R where I (from the French word intensité) represents current, V is voltage, and R is resistance.
The simplest circuit consists of a voltage source connected to a resistance. We call this a series circuit because there is only one path for current to flow—current leaving one terminal of the voltage source has no place else to go but through the single resistor on its way back to the other terminal of the source. Current in amperes is equal to the voltage in volts divided by the resistance in ohms. If our circuit consists of a 12 volt battery and a 10 ohm resistor, we’ll have a current of 1.2 amperes flowing in the circuit.
Since Ohm’s Law is an algebraic equation, if you know any two values you can calculate the third one. Suppose the battery is unmarked. If you connect an ammeter into the circuit and measure the current, you can calculate the voltage. Or if the resistor is unmarked, you can calculate the resistance if you know the voltage and current.
By the way, in order to connect that ammeter, you’ll have to break the circuit and connect the meter terminals to the two free ends you’ve just created. Since an ammeter measures current flow, the current must flow through the meter itself in order to make a measurement.
An extension of Ohm’s Law sometimes known as Watt’s Law is that electrical power, the measure of the actual work that can be done by electricity, is equal to the voltage times the current. P=V x I is how it’s normally written.
Getting wet again temporarily, power is analogous to the amount of water that actually comes out of the bucket in a given amount of time—gallons per minute if you will. In our simple circuit, we’re putting 14.4 watts (12 volts times 1.2 amps) into our resistor. By the way, that’s a lot of power for a resistor that you typically find on a circuit board, but relatively small compared to the power delivered to a loudspeaker in a PA system.
The interrelationships expressed by Ohm’s and Watt’s laws can be used to calculate many useful things. Remember this voltage/current/power relationship next time you wonder whether that unmarked wall wart you found in the box marked “Stuff Too Good to Throw Away” is properly sized for powering the gadget that you just bought which came without a power supply.
A more practical circuit
Now let’s make our simple circuit a little more complicated by putting a second resistor in the current path. We say that the two resistors are in series since the same current flows through both. It’s easy to see that the total voltage across the pair of resistors is equal to the applied voltage, but what’s the voltage across each of the two resistors?
Since the same amount of current must flow through both resistors in the series circuit, by knowing the current, we can calculate the voltage across each one. Let’s say that R1 is 90 ohms and R2 is 10 ohms. Since for resistors in series, the total resistance is the sum of the individual resistances, we have a total resistance of 100 ohms connected to our 12 volt source, giving a current of 0.12 A. That’s 120 mA—a milliampere (mA) is 1/1000 of an ampere.
Rearranging the terms in the Ohm’s Law equation allows us to solve for voltage if we know the current and resistance. Algebra (and perhaps your memory of high school physics) tells us that V = I x R, so we’ll have 10.8 volts (0.12 amps times 90 ohms) across resistor R1 and 1.2 volts (0.12 amps times 10 ohms) across resistor R2. Note that the sum of the voltage drops across the two resistors is equal to the applied voltage. We haven’t lost anything, so our calculations are valid.
The practical application for this circuit is called a voltage divider. One example is a circuit to reduce the output voltage of a “pro” piece of audio gear down to “consumer” level.
Now let’s look at a circuit that has more than one path through which current can flow. Let’s connect our two resistors across our voltage source, so now we have two loops. We say that the two resistors are connected in parallel because they both have the same voltage across them. The current flowing out of the battery reaches the junction of the two resistors and splits off into two branches with some current flowing through each resistor.
The amount of current flowing through each resistor is proportional to its resistance. Since each resistor is connected to the same voltage source and we know the value of the resistor, we can calculate the current in each of the branches. The current (I1) flowing through R1 is 0.133 amps (12 volts / 90 ohms) while the current (I2) flowing through R2 is 1.2 amps (12 volts / 10 ohms). The total current flowing from the battery is the sum of those two currents, or 1.333 amps.
Note that connecting a resistor in parallel with another causes additional current to be drawn from the source. Therefore the total resistance of resistors in parallel must be less than that of any one of the resistors alone.
Functions at the junction
While Mr. Ohm gets most of the credit, these two examples illustrate another pair of laws that are fundamental to circuit theory. Kirchoff’s Current Law states that for every junction in a circuit, the sum of all currents entering and leaving that junction is zero. This simply means that all the current that goes into a junction must leave it.
If you know the currents that branch off from a junction to different components, you can determine the current entering the junction. Similarly, if you know the current entering a junction, you know that no matter how many branches split off from it, the sum of the currents in each of those branches must equal what’s going into the branch. While this may appear to be an obvious or abstract concept in itself, it can help you to determine what’s drawing too much or not enough current when trying to troubleshoot a piece of equipment.
This is a good time to bring up the concept of conventional current flow. We use the term “conventional” not in the sense of “normal,” but rather, in the sense of establishing a convention for measurements and circuit analysis. Electrons are negatively charged, which causes them to naturally flow toward a positively charged point; however, we consider conventional current flow to be from positive to negative just because it makes more sense.
In our sample circuit, if the top terminal on our voltage source is positive, the conventional current flow will be in the clockwise direction. By establishing, at least on paper, the direction of current flow, we can always define whether a current is entering or leaving a junction.
There’s a second law that bears Kirchoff’s name. This one has to do with voltages, and it states that the sum of all the voltage changes across every component in a circuit must equal zero. Since the voltage source is considered to be a component, it’s a bit clearer to look at this another way, saying that the sum of the voltage drops of components in series across a voltage source must equal the source’s voltage. In our voltage divider example, you can see that the voltages across R1 and R2 add up to the source voltage.
These two laws are useful in preserving your sanity when trying to work out what happens when you have a combination of elements in series and parallel. Just remember—current and voltage can’t just appear or disappear at junctions or inside components, so everything has to balance out.
AC circuits: getting into impedance
Voltage (and its corresponding current) can be either direct or alternating. A direct current maintains the same polarity, and therefore the same direction of current flow, at all times. With an alternating current source, the polarity reverses direction periodically—60 times per second for the utility power in North American homes, 440 times per second for the signal from a pickup when we play an “A” on an electric guitar, and so on.
It’s much easier to talk about DC circuits than AC since conditions don’t change every time you turn around. This is why our examples here have all assumed direct current. Resistors behave the same in both AC and DC circuits, but the behavior of capacitors and inductors changes over time.
That’s important to understand, because capacitors and inductors are basic components in many types of audio gear. For example, remember that another word for capacitor is “condenser” and have a look in your mic closet to see a whole bunch of capacitor-based devices that you rely on, and then realize that transformers are inductors, as are the pickups on an electric guitar.
The characteristic that describes the behavior of those components in an AC circuit is impedance, and the math involved is a bit more complicated than with simple resistance. Still, since we spend a lot of time in our day-to-day studio life talking about high-impedance this and low-impedance that, it’s worth understanding the basics of how these components’ impedance affects audio.
Mike Rivers isn’t Mixerman. Really. You can contact him at firstname.lastname@example.org