Electrical Fundamentals

 

AA Battery

A typical AA battery (a rechargeable NiMH one)

Since much of the subject matter relating to fan controllers requires a basic understanding of electrical power, I thought it might be edifying to review some of the basic concepts of electricity.

Electric charge is a property of subatomic particles (most notably, the proton [+] and electron [-]). The presence of a charge gives rise to the electromagnetic force, one of the four fundamental forces in nature. The amount of charge is usually expressed in coulombs. Voltage is the electrical potential difference between two points, or the difference in electrical potential energy between two points. This is measured in joules per coulomb, or volts. Measuring voltage requires connecting the two leads of a voltmeter (positive and negative leads) to the two points across which voltage is to be measured. This, to measure the voltage of a battery, one lead is connected to the positive terminal of the battery and the other lead is connected to the negative terminal. A common use of the term voltage is in describing the voltage dropped across an electrical device (such as a resistor). The voltage drop across the device can be understood as the difference between measurements at each terminal of the device with repsect to a common reference point or ground. The voltage drop is the difference between the two readings. Two points connected by a conductor without resistances and not within a changing magnetic field have a voltage of zero. The conventional symbol for voltage is V.

Multimeter

A typical digital multimeter, which can be used to measure voltage and current.

A second important concept is current, the flow of electric charge. Electric charge flows when there is a voltage preent across a current. It is measured in coulombs per second, or amperes. Electrical conductance is the ease at which an electrical current passes. There are two primary forms of current: direct current (DC), the unidirectional flow of electric charge (usually found in batteries, thermocouples and solar cells), and alternating current (AC), in which the movement of electric charge periodically reverses direction (the form of power usually delivered to businesses and residences). The conventional symbol for current is I.

If there is electrical conductance, then there must also be an inverse quantity: electrical resistance, the opposition to the passage of electric current, which is measured in ohms. The key relation between voltage, current, and resistance was discovered by Georg Ohm in 1827 and is expressed as Ohm’s Law:

V = I * R

or voltage equals current times resistance. Thus the current between two points is directly proportional to the potential difference across the two points (and inversely proportional to the resistance). Although this relationship seems somewhat obvious, the discovery of Ohm’s law was a major development in the history of electronics.

Resistor

A typical 470-ohm resistor.

When electrical charges move through a circuit where there is an electric potential difference, the potential does work on the charges, converting the energy into kinetic energy. The unit of power in physics is joules per second (J/s), or watts. The conventional symbol for power is P. You may have guessed already that power between two points in a circuit can be measured by multiplying current in amps (coulombs/sec) by the voltage in volts (joules/coulomb), which leaves us with joules per second (power in watts). Thus:

P = V * I

This is known as Joule’s Law, which gives us a measure of the dissipated power between two points in a circuit. By combined Ohm’s Law with Joule’s Law, we can obtain an alternate way of expressing the dissipated power:

P = (I * R) * I = I^2 * R

These basic equations give us enough information to do some quick-and-dirty calculations with fan controllers. Assume that we have 4 fans to control, and each fan uses half an amp (.5 A) The total current used by the fans is thus .5 A * 4, or 2 amps. Let us also assume there is a 4-channel, 45-watt fan controller available. Using Joule’s Law,

p = V * I, or I = P/V

Thus, we can calculate how much current the controller can handle by dividing the power by voltage. Since the controller is 45 watts, and each fan uses 12 volts of DC power, I = (45 W/12 V) = 3.75 A. Therefore, the controller has more than enough power to handle the 4 fans.

An electric circuit is an interconnection of electrical components such that an electric charge is made to flow along a closed path, usually to perform a useful task. COmponents can include resistors, capacitors, switches, transistors and transformers, but for purposes of this introductory article, I will focus on the resistor. The resistor is a passive element (it consumes and does not produce energy), and, as the name suggests, it resists the current through it, dissipating its energy as heat. The resistance is a consequence of the motion of charge through a conductor. The resistance of most materials is relatively constant over a range of temperatures and currents; materials is relatively constant over a range of temperatures and currents; materials under these conditions are known as “ohmic”. In a fan controller, resistors will often be used to reduce the voltage to a fan; however, since the resistor dissipates energy as heat, the buildup of heat is often a concern.

I may write a follow-up article to further explain electronic components, but this should be enough basic concepts for the uninitiated reader to understand the fundamentals of fan controllers. Any feedback on this article would be greatly appreciated.

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