Basic Circuit Theory

This guide is in no way intended to be an end all, be all, one stop shop for understanding electricity. Unless you are some sort of Tesla-esque super genius, it will probably takes years of study to even begin to really understand how electricity works and the seemingly limitless possibilities which lie within. With that said, I have created this guide in hopes of illuminating a few of the most basic principles for those who are looking for an electrifyingly awesome hobby.

## Going With the Flow

Electricity (at least the kind we are concerned with here) can really be summed up with one simple phrase: the flow of charged particles through a medium. I know, if it's really that simple, then why do electronics seem so complicated? Because they are complicated. Designing a circuit is all about how to control and manipulate that flow of charged particles. Now, because this is not meant to be an in depth study of physics or a theoretical debate as to whether of not electricity is the flow of electrons trying to find holes to fill, or the flow of holes trying to find electrons to fill them, I will simply leave it as this:

Circuit design is all about controlling the flow of electricity.

This flow, known as current, is measured in amperes - amps for short. Current is the measurement of how many coulombs (6.241 x 1018 electrons) move through a point every second. The amount of available energy (SI unit: Joule) in each coulomb is known as voltage and is measured in volts. Voltage represents the energy potential available in an electric current. To actually control the flow, there needs to be some resistance. This resistance, measured in ohms (Ω), is how difficult it is for current to flow and is the inverse of electrical conductance - how easy it is for current to flow - measured in siemens. Combining these concepts together gives us power which is measured in watts. Increasing either current or voltage will increase power, but proper balance must be attained.

These basic relationships between voltage, current, and resistance are known as Ohm's Law and will be the building blocks of almost every circuit analysis you will ever do. I say almost because not everything will follow these rules exactly, but in most cases, an approximation can be made. Besides, rules were made to be broken! Anything which maintains it's resistance regardless of the voltage or current applied, the charge polarity (direction of current), or if it is an alternating or direct current is considered to be "ohmic."

Ohm's Law:     V = I / R ;     I = V / R ;     R = V / I

There are a couple of other concepts which are very important to circuit design. The first is capacitance - the ability to store energy in an electric field - measured in farads. The second is inductance - the ability to store energy in a magnetic field - measured in henries. These two concepts involve a change in electricity over time and can be somewhat difficult to comprehend. In a DC circuit, a capacitor can been seen as an "open" because it blocks all current, while an inductor can be seen as a "short" because it allows all current to pass through.

## The Water Analogy

Comparing electricity to a water system can be a great way to help demystify it by explaining it in terms of something much more easily understood. Love it or hate it, the water analogy has helped me many times in both explaining things to someone and understanding things myself. The problem with it is that the terms can be easily confused and are often explained incorrectly. I will attempt to build a circuit piece by piece and explain how it correlates to water. Current is the easiest thing to compare because it means the amount of something flowing per second in both electricity and water. A fast moving stream has high current, just like a lot of electrons flowing through a wire.

The first thing needed is a source for the potential such as a battery. This is equivalent to a water pump. Note, I did not say this was a source of the electricity/water itself, just the force behind it. A water pump takes a low pressure input and pumps it through the pipe as high pressure water. A battery does basically the same thing. Higher voltage is like having higher water pressure. It will want to move quickly because it has a lot of potential energy. While water flows through a pipe, electricity needs some medium with a high conductivity (low resistance) such as metal. Using something with a high resistance is like trying to pump water through a piece of wood. It will eventually make it through, but will take a long time for anything to flow at all. Copper wire is a good place to start.

The circuit has to be completed for anything to flow. This means that the wire has to eventually connect back to the second battery terminal; however, directly connecting the positive and negative terminals will result in a short circuit, draining the battery's potential very rapidly. Also, because the wire has a very low resistance, equation 3 from above tells us that the current will be incredibly high. If the wire was not designed to handle such a high current, it will overheat and eventually catch on fire. This is like trying to pump a lot of water through a very small hose; it will eventually bulge and burst from the pressure.

But don't get confused by the wording here. "Pressure" is used to describe the voltage, not the current. So by having an incredibly low voltage source, a short circuit will do less damage because there is less potential for a high current flow; otherwise, there must be some resistance to limit the flow through the circuit. Anything placed in series with the wire will act as resistance - lights, motors, heating elements, etc. This is like having a stretch of pipe much smaller than the rest in the middle of the water system. As only so much water can be in the pipe at once, it will limit how much water is flowing through it at any given time.

According to Ohm's Law, increasing the resistance with a
constant voltage will decrease the current, and vice versa.

Lastly, a circuit has a ground or reference point. This is similar to the water reservoir that the pump initially uses as a water source. Once the pipe is full of water, the connection to the reservoir could be removed without ill effect. Likewise, the ground wire on a circuit could be broken, and the circuit would continue to function. However, it is desirable to maintain constant reference to the voltage of the earth. This will also protect against electric shock, giving the excess current a path away from the circuit, and can help in shielding the circuit from outside interference. The "earth ground" is not to be confused with "circuit ground" which is the common node of the circuit typically connected to the negative terminal of the voltage source. Although earth ground and circuit ground are often shorted, they are not the same thing.

## Types of Current Flow

The last thing I want to talk about here is the difference between alternating current (AC) and direct current (DC) circuits. The most common DC power source is a battery. When a resistance is connected across the battery terminals, a constant flow of current will be seen through the resistance. The only reason for this current to change is with the eventual decrease of potential in the battery, but that's a completely different subject because batteries are non-ohmic components. A more ideal example is a DC power supply which converts an AC or DC power source into a DC voltage. As long as the necessary input remains, a constant voltage level is available and therefore current will constantly flow.

Direct current flows in one direction.

The most common AC power source is the wall outlets seen in a typical home. Plugging a device into the outlet will complete the circuit and allow current to flow; however, this current is not constant over time because the voltage of the source changes with time. In the case of a wall outlet in the USA, the voltage will alternate from +120 Vrms to -120 Vrms 60 times per second (60 Hz). The negative voltage implies that the current actually switches direction halfway and flows in the opposite direction through the circuit. Anything with a voltage that changes over time because of a reversal of current direction is considered an AC circuit.

Alternating current periodically reverses direction.

Power is transmitted using AC because it can be sent over vast distances using very high voltages with little line loss; but most all consumer electronics require low voltage DC power and therefore must have some sort of voltage converter and/or regulator built in. There will also be some inefficiency in the conversion of one type of current or voltage level to another. Typical forms of power loss are heat dissipation and motion. The latter of these is actually what causes the hum often heard from electric transformers because the iron core of these devices will slightly change shape as the current flow reverses, generating an audible tone.

Equations

There are a lot of equations used in circuit analysis, many of which use the same symbols to represent multiple things. Note: a "d" in front something (dx) is actually the change in that unit over time. (Δx(t) dt).

Current (I) in Amps =
Coulombs (q) per Second
I = q / s        (1)

Voltage (V) in Volts =
Joules / Coulomb (q)
V = J / q       (2)

Resistance (R) in Ohms =
Voltage / Current
R = V / I        (3)

Power (P) in Watts  =
Voltage * Current
P = J / s        (4)
P = V * I        (5)
P = I2 * R        (6)
P = V2 / R        (7)

Coulombs (q) / Volt
C= q / V        (8)

Inductance (L) in Henries=
Webers (Φ) / Ampere
L = Φ / A     (9) 