Thursday, September 21, 2006

Tech Corner: Capacitance, Part I Introduction Up until now we’ve been focused on simple circuit properties, including voltage, current, and resistance. Now that we’ve got that knowledge in our back pockets, we’ll move on to some more advanced properties of electric circuits. In the next few editions of Tech Corner we’ll focus on an electrical element known as a capacitor. A capacitor is an energy storage element. It actually takes energy and stores it in the form of an electric field. Read on to learn more! Let’s Get Physical A capacitor is a relatively simple device to create. . .all we need are two conductive materials that are separated by an insulator. You remember from previous entries that a conductor permits the flow of electrons with relative ease while an insulator prohibits the flow of electrons. In its simplest terms, a capacitor is a component that consists of two conductive plates separated by an insulating material, often referred to as a dielectric (di meaning two, as in two conductors). This insulating material can be any type of insulator, including air. The strength of a capacitor is measured in Farads (F) and is directly related to the surface area of the two plates as well as how closely they are spaced together. Figure 1.0: Electrical Symbol and Sample Capacitors When All Else Fails, Charge It! A funny thing happens when we apply a DC voltage to a capacitor. The plate connected to the negative (-) side of the voltage source obtains a net negative charge as the electrons disperse onto the surface area of the plate. The plate connected to the positive (+) side of the voltage source obtains a net positive charge while since the electrons on the plate are attracted to the positive (+) terminal of the voltage source. What’s important to note is that the insulator between the plates keeps electrical current from flowing through the capacitor, rather, the electrons move onto the plates and begin to build up a strong electric field, or voltage. Figure 2.0: Charging Current in a Capacitor The plates will continue to soak up charge until the voltage across the plates equals the source voltage. The act of the electrons dispersing themselves onto the conductive plates is known as charging and the associated current required to charge the plates is known as charging current. Charging current is very high the instant we apply a voltage to the capacitor and slowly falls to zero as the voltage across the capacitor reaches the source voltage. At this point no more electrons can flow and the capacitor is said to be charged. Figure 3.0: Charging Current vs. Time Overnight Storage Please So what now? Well that’s just the thing – all that energy is now stored in the capacitor ready and waiting. And there it will sit, even if we disconnect the voltage source from the capacitor. Since the electrons have no way of moving from one plate to the other through the dielectric, the capacitor will store all of this energy indefinitely*. In order to utilize this energy we need to connect some sort of path for the energy to move. If we connect a resistor, R, across the terminals of the capacitor, the energy will discharge through the resistor in the form of electric current. This current will continue to flow until the voltage across the plates falls to 0 and no more energy is stored in capacitor. *Since there is no such thing as a perfect insulator, some current will leak through the dielectric and the capacitor will eventually discharge all of its energy. This will take a very long time depending on the resistance of the dielectric material. Figure 4.0: Capacitor Discharging Through a Resistor Conclusion Capacitors are so important in the world of electronics because of their unique property to store energy for a given period of time. The rate at which the capacitor charges up and discharges is also variable, and is used to alter the timing in many circuits from elevator lights to windshield wipers. But, as we will soon learn about, capacitors behave in different ways depending on whether an AC or a DC voltage is applied across their plates.

Thursday, June 01, 2006

Tech Corner: Power Factor Introduction Now that we know what the phase angle between a voltage and current waveform is we can learn about another important principle in electronics: power factor. Power factor is very important when trying to calculate the power delivered by a source or absorbed by a load. So read on my friends and expand your electronic vocabulary, for in this entry of AR’s Tech Corner we’ll discuss power factor. Definition Time Power factor tells us how resistive a circuit is. Depending on the various components in a circuit it can have a certain element of resistance and reactance. Resistance is created by resistors, or insulating materials that resist the flow of electric current. Reactance is created by circuit elements such as inductors and capacitors, which introduce reactance into a circuit. Reactance causes the voltage and current waveforms in a circuit to shift out of phase from each other. We will discuss these circuit components in later entries. A circuit’s power factor can fall anywhere within a scale of 0 to 1. A circuit with a power factor of 1 is said to be purely resistive while a circuit with a power factor of 0 is said to be purely reactive. All circuits fall somewhere in between these two extremes. Let’s elaborate. Relationships are Key Power factor is the cosine of the phase angle. Easy. . .take a deep breath and I’ll say it again. Power factor is the cosine of the phase angle. See! There’s nothing to it. If we know what the phase angle between two waveforms is we can easily find the power factor. Let’s try it. Figure 1.0: Voltage and Current Waveforms in a Purely Resistive Circuit We can see in Figure 1.0 that the phase angle between the voltage and current is 0 degrees since they are in phase with each other. This also means that the circuit is purely resistive since voltage and current are proportional to each other at all points of the waveform. Phase angle = 0º Cos (0º) = 1 A power factor of 1 means that the circuit is purely resistive. Congratulations – you just calculated your first power factor. Let’s do another. Figure 2.0: Voltage and Current Waveforms in a Purely Reactive Circuit We can see in Figure 2.0 that the phase angle between the voltage and current is 90 degrees. This also means that the circuit is purely reactive since the voltage is at its maximum when the current is at its minimum. Phase angle = 90º Cos (90º) = 0 A power factor of 0 means that the circuit is purely reactive. Nothing to it! Conclusion So why is power factor important? Anytime energy is delivered it is beneficial that the power factor is as close to 1 as possible. A power factor that is close to 1 means that the voltage and the current are both at their maximum point at the same time – in this scenario the maximum energy is delivered to a load (current) when there is maximum potential across the load (voltage). This is especially important in the utility power industry when lots of energy is being delivered across vast distances.

Tuesday, May 02, 2006

Tech Corner: Phase Angle Introduction Now that we are moving into more advanced concepts in electronics we need to discuss a few more principles. We’ll start with what is known as phase angle. I know, it sounds like some crazy geometric principle from high school, but I assure you dear reader, it is very important when dealing with every day circuits. So let’s knock this out of the way and get onto the good stuff! In this edition of AR’s Tech Corner we’ll be discussing phase angle. AC Review Phase angle is a concept that only comes into play in AC circuits, or more specifically, circuits with AC voltages and currents. Remember that an AC voltage changes with time and can be many different types of shapes. For the purposes of this entry we’ll deal with a sinusoid, see Figure 1.0 below. Figure 1.0: AC Voltage or Current The image above represents one full cycle of a sine wave. For more on this refer to the Tech Corner entry on AC/DC Sources. Pulling a 180º In electronics we ascribe a certain degree value for each point in an AC waveform. Initially the sine wave is at 0 which corresponds to 0 degrees. The positive peak sits at 90 degrees. The next zero-crossing in between the peaks is 180 degrees. The negative peak is at 270 degrees, and the next zero-crossing is at 360 degrees. So you can think of it like this: 1 full cycle of the AC waveform represents 360 degrees. These values are made regardless of the frequency of the waveform and are known as the phase of the waveform. Figure 2.0: Degree Measurements of a Sinusoid Fire Phasors! So why are these degree values important? Well they become very helpful when discussing the relationship between current and voltage in a circuit. Figure 3.0 shows a simple circuit containing an AC voltage source and a resistor. Using Ohm’s Law we know that the voltage and current are directly proportional to each other (V=I*R). Figure 3.0: A Simple Circuit So let’s take a look at the current and the voltage waveforms in this circuit. Figure 4.0: Voltage and Current Waveforms in Phase You can see that the voltage and the current in the circuit track each other point for point throughout an entire cycle. These two waveforms are said to be in phase because there is no difference when each reaches a peak or a zero. And so their phase angle, or difference in their phases is 0. This holds true in all purely resistive circuits since we know that current and voltage are proportional at all points of the AC waveform. Likewise, voltage and current waveforms can be out of phase. Figure 5.0 shows voltage and current waveforms that are 180 degrees out of phase with each other. Figure 5.0: Voltage and Current Waveforms with Phase Angle of 180º The phase angle of these two waveforms is the difference in their phases. So in this case we say that the phase angle between the voltage and the current is 180 degrees. Wrap it Up Due to the nature of electric circuits, the phase angle between voltage and current waveforms can be anywhere within the 360 degrees of an AC signal’s cycle. In later entries we’ll discuss capacitors and inductors, two circuit components that create 90 degree differences between the voltage applied across them and the current flowing through them. So put phase angle in your back pocket, dear reader, for you are now armed with this dangerous weapon at your disposal!

Monday, February 20, 2006

Tech Corner: Special Application - The Voltage Divider One of the most basic and widely used circuits in all of electronics is the “voltage divider.” This circuit converts an input voltage of one value to an output voltage of another level. Look closely at Figure 1.0 below and you will see something very familiar. Figure 1.0: Voltage Divider Circuit Notice anything familiar? It’s simply a series circuit! There is a voltage source and two resistors. We need to calculate what the voltage is across the 5 Ω resistor? Piece of cake right? Right! Find the current, I. Find the output voltage, Vout. 1.) In order to calculate the current, we can simplify the circuit by adding the resistances together to 1 equivalent resistance. Rt = R1 + R2 Rt = 15 + 5 = 20 Ω 2.) We can now use Ohm’s Law to calculate the current flowing through the circuit. V = I * R 20 = I * 20 I = 1 amp 3.) Vout is simply the voltage drop across the 5 Ω resistor. We can use Ohm’s Law to determine the voltage. Vout = I * R Vout = 1 * 5 Vout = 5 volts Voltage Divider Shortcut The method above methodically explains the how and why solving a voltage divider circuit. Now that you understand this I can show you a shortcut that will work for any voltage divider: Vout = Vin * [R2 / (R1 + R2)] where R2 is the resistor whose voltage drop you want to find

Thursday, February 09, 2006

Comments/Questions/Suggestions? Hello again readers. I wanted to take this opportunity to thank you for your time. This blog has been somewhat of an experiment thus far and I am pleased with how it is going. I'd like to encourage any and all readers to leave comments on new or old posts. You can do this by clicking on the "comment" link at the bottom of each entry. Feel free to ask questions about anything and everything related to the safety testing industry. Are there any suggestions you have for what is working and what is not? Is there something I haven't covered that you'd like to see? Tell me! With your feedback, I can help to tailor the blog to cover topics that interest you, not me. Thanks for reading, Adam

Friday, January 27, 2006

Tech Corner: Series and Parallel Circuits Introduction Welcome back readers! Several entries ago we discussed the basic concepts of resistance and Ohm’s Law. As promised, in this edition of AR’s Tech Corner we are going to use what we’ve learned to explore more advanced concepts in circuit theory: series and parallel resistive circuits. Using Ohm’s Law you are going to be able to solve more difficult circuit problems and hopefully gain a better understanding of the way some common electrical products work. If you need a refresher before we begin, please refer to the entries on resistance and Ohm’s Law before proceeding. Enjoy! Review: A Simple Resistive Circuit and Ohm’s Law According to Ohm’s Law, when a voltage is placed across a resistor a current will result. Figure 1.0: A Simple Resistive Circuit In the case of this circuit Ohm’s Law tells us that the voltage, V, will be equal to the product of the current, I, and the resistance, R. V = I * R Thus if we know 2 of the variables in the above equation we can always find the 3rd. Series and Parallel Resistances So what happens when we have a circuit that contains more than one resistor? How are we to know what is going on? It turns out that resistors can be placed in one of two configurations: series and parallel. Figure 2.0 (a): A Simple Series Circuit Figure 2.0 (b): A Simple Parallel Circuit Series Circuits Resistors are said to be in series when they both share one common point and allow current to flow through only one path. Note that in Figure 2.0(a) both resistors are connected together at their inner-most ends, while their outer-most ends are connected to either side of a voltage source. Since current must flow through a loop and only one loop exists, the current, I, must flow through both resistors. In a series circuit, current is the same through all circuit components. If the same current flows through both resistors in the above circuit the total resistance to the flow of electrical current is the sum of both resistances. This leads us to another important rule of series circuits: In a series circuit, the total resistance is the sum of the individual resistances. So in the circuit in Figure 2.0(a) we can add both resistors of value R, yielding a total resistance of 2R. We have now simplified the circuit to one resistor, 2R, and can use Ohm’s Law to calculate the current and the voltage. Of course, since the same current flows through each resistor, then a voltage drop will appear across each resistor according to Ohm’s Law. Depending on the values of the resistances, the voltage across each resistor can be different. In this case, however, since both resistances have the same value of R, the voltage will drop equally across each resistor. This leads us to the third and final important rule of series circuits: In a series circuit, the sum of the voltage drops across each resistor must equal the source voltage. Let’s do an example to help you better understand these concepts. Series Circuit Example Calculate the current, I, flowing through the circuit above. Calculate the voltage drop across each resistor. 1.) Since we know that resistors in series add, we can add both resistors to get a single value. R1 + R2 = Rt 8 + 2 = 10 Ω 2.) Since a voltage of 10 volts is applied across our total resistance of 10 Ω, we can use Ohm’s Law to find the current, I. V / R = I 10 / 10 = 1 amp 3.) To calculate the individual voltage drops we use Ohm’s Law. I * R = V V1 = 1 * 2 = 2 volts V2 = 1 * 8 = 8 volts Parallel Circuits Resistors are said to be in parallel when they are connected together at both ends, allowing current to flow through more than one path. Note that in Figure 2.0(b) the top ends of the resistors are connected together and to one side of the voltage source, while the bottom ends of both resistors are connected together and to the other side of the voltage source. The voltage source is being applied to both resistors equally. In a parallel circuit, the voltage across each circuit component is the same. If the voltage across each resistor is equal to the source voltage, then the current going through each individual resistor can be calculated separately using Ohm’s Law. Further, we know that the total current coming out of the source equals the sum of the currents going through each resistor (for more on this see the Tech Corner article on current). In a parallel circuit, the sum of the current going through each resistor must equal the total current supplied by the source. In Figure 2.0(b) you can see that there is a total circuit current, It, coming from the source. The current then splits and I1 and I2 each flows through one of the resistors, R. The total current, It, is equal to the sum of the individual currents, I1 and I2. Just as with resistors in series, there is a shortcut for finding the total resistance in a parallel circuit. The formula is somewhat more complex, but can be used to simplify circuits with many resistors in parallel. The formula is as follows: Rt = 1 / [(1 / R1) + (1 / R2)] For every extra resistor in the circuit, another fraction can be added within the equation’s brackets. It’s simply plug and chug!! Let’s do an example to help you better understand these concepts. Parallel Circuit Example Calculate the total current, It flowing to R1 and R2. Calculate the current flowing through R1 and R2. 1.) First we use our formula for calculating the total resistance in a parallel circuit. Rt = 1 / [(1 / R1) + (1 / R2)] Rt = 1 / [(1/10) + (1/15)] = 6 Ω 2.) Since we know the total resistance of the circuit and the voltage, we can use Ohm’s Law to calculate the total current leaving the source. V = It *R 18 = It * 6 It = 3 amps 3.) In order to find the individual currents going through each resistor we can use Ohm’s Law again. V = I1 * R1 18 = I1 * 10 I1 = 1.8 amps V = I2 * R2 18 = I2 * 15 I2 = 1.2 amps Conclusion Resistors come in all shapes and sizes, yet they can only be arranged in two configurations within a circuit. The ability to mathematically reduce many resistors down to one is useful skill in circuit design. Armed with your new knowledge of series and parallel resistive circuits, and the ability to simplify a complex string of resistances, there is no limit to the places you can go in the world of electronics!!!

Monday, January 23, 2006

Tech Corner: AC/DC - No It's Not Just a Band Part 2 Introduction The story goes like this. Angus and Malcolm Young (AC/DC’s guitar players) were trying to think of a name for their new band. They happened to look at a label on a nearby electrical product and saw the following: AC/DC. The rest is history and one of the greatest hard rock bands was formed. Yes money talks and we’ve all rocked out to “You Shook Me All Night Long”, but what does AC/DC really mean? This is the topic of discussion in this edition of AR’s Tech Corner. Explanation Station AC/DC is an acronym for Alternating Current/Direct Current. Alternating and direct are the two general descriptions used to describe the shape of electrical waveforms. These waveforms can be either a current or a voltage depending on the type of power source used and the type of load that is absorbing power. In Part 2, we will discuss Alternating Current. Characteristics of Alternating Current AC Waveform – a cyclical electrical signal that, over time, changes in both magnitude and polarity. Example: utility power - wall outlet. Magnitude (amplitude) – the intensity of an electrical waveform measured in volts or amps. Represented graphically by the signal’s distance from neutral. Polarity – a signal’s charge as related to neutral. Can be either positive or negative. Alternating Current is a bit more involved since the signal can change in both magnitude and polarity with time. An AC waveform also has one more important distinguishing characteristic: AC waveforms are cyclical, meaning that they repeat with time. There are many types of AC waveforms that are used for different purposes: square waves, triangle waves, ramp waves, etc; however, the sine wave is perhaps the most common type of AC waveform. Figure 1.0 below shows a sinusoidal waveform, or sine wave. Due to the way modern day generators (rotating devices that convert mechanical energy to electrical energy) work, sine waves are used as the utility power waveform in many countries around the world including the United States. Interestingly enough, AC signals are the only signals capable of being manipulated by transformers (a device we will discuss in later sections), another reason why sine waves are common place in utility power. Figure 1.0: A Sine Wave See the Sine, Be the Sine You can see that the sine wave initially starts at a value of 0, rises to a maximum positive value (we call this point the peak), falls back to 0, lowers to a negative peak, and again rises to 0. The top half is identical to bottom half, and the magnitude of the wave follows the function y = sin (x). If you remember your trigonometry this formula might look familiar to you. {Sin is a mathematical principle that relates one angle of a right triangle to the side opposite the angle and the triangle’s hypotenuse.} Once the negative peak rises up to 0, the entire waveform is repeated. The number of cycles that repeat per second is known as the frequency of the AC waveform. Frequency is measured in Hertz (Hz) and 1 Hz = 1 cycle/second. In the U.S., utility power is produced at a frequency of 60 Hz. Figure 2.0: Frequency Sine Wave Measurements Both current and voltage can be sinusoidal, and when we refer to a sinusoid there are several measurements we can use. First we can refer to the peak value of the sine wave. If we have a 120 voltpeak sinusoidal source, the peaks of the sine wave are 120 volts greater and less than 0 (the positive peak is +120 volts and the negative peak is -120 volts). Another measurement used to describe a sine wave is the peak-to-peak measurement. In this case it would be 240 voltspeak-to-peak since the positive peak is +120 volts and the negative peak is -120 volts. Figure 3.0: Sine Wave Measurements Since the average value of a sine wave is 0 (the signal spends equal amounts of time with a positive and negative value) we need another way of determining the amount of energy a sine wave can supply to a load with time. This measurement is called the Root Mean Squared (RMS) value. The RMS value equates the amount of energy delivered by an AC source to that of a DC source. Simply stated, this means that a 120 voltrms sine wave will deliver the same energy to a load as a 120 volt DC source. Most voltages are given in RMS values. As an example, take a common wall outlet. In the U.S. most wall outlets are rated at 120 volts. This is an RMS measurement; the peaks of the sine wave coming out of the outlet are actually higher than ±120 volts. How much higher? The answer is 1.414 times higher. The way to relate the peak of a sine wave to its RMS value is by multiplying the RMS value by 1.414. Vpeak = Vrms * 1.414 Sine Wave Current When a sinusoidal voltage is applied across a resistor, a sinusoidal current develops according to Ohm’s Law. What is unique to this application of voltage is that the current reverses each direction as the voltage changes polarity. During the first half of the cycle, the voltage climbs from 0 volts to its positive peak, and back down towards 0. The resulting current flows clockwise in Figure 4.0. Once the sign wave crosses 0 volts the voltage reverses polarity and descends to negative peak before returning back to 0. The resulting current flowing at this time travels counterclockwise. Figure 4.0: Current Flow Direction from a Sinusoidal Voltage Source For a split second the current falls to zero as the voltage reverses polarity. If the lights in your home are run off of a wall outlet operating at a frequency of 60 Hz, they are actually turning on and off 120 times per second but your eyes aren’t fast enough to detect the change! Conclusion Whew! Take a deep breath reader for you’ve come a long way. In this two-part lesson you’ve learned about the two types of voltage waveforms and their properties. Now that you’ve got this under your belt we can move on to some very interesting concepts in the next editions of AR Tech Corner.

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