# ATAT 105 Basic Electricity > # [[T105 Week 9| ◀️ ]]  [[T105 Home| Home ]]  [[T105 Week 11| ▶️ ]]               [[QR T105 Week 10| 🌐 ]] ># [[T105 Week 10|Week 10]] >- [[T105 Week 10#Capacitance|Capacitance]] >- [[T105 Week 10#Types of Capacitors|Types of Capacitors]] >- [[T105 Week 10#Capacitors in Circuits|Capacitors in Circuits]] ># [[T105 Week 10#Lab|Lab]] >- [[T105 Week 10#Build an RC Circuit|Build an RC Circuit]] >[!jbplus|c-blue]- Lesson Intro >### What >In this lesson you will learn about capacitors in preparation for learning about alternating current. > >### Why > >The dynamic aspect of capacitors must be understood in order to analyze Alternating Current circuits. > > >## Approach and Objectives > >By understanding the following topics, you will have achieved the learning outcome for this lesson. Consult your course outline for the learning outcomes and other details of this course. > >### Course Learning Objectives > >CLO 13. Compute the peak, instantaneous and effective (RMS) values of an AC sine wave. >CLO 14. Show using an oscilloscope the measurement of frequency, period and voltage of an AC waveform. >CLO 16. Calculate total capacitance in series and parallel capacitive circuits. > > >### Testing > >You will be tested on this material on the midterm test and the final test. Details [[T105 Intro#Testing and Grades|here]]. >[!jbplus|c-blue]- Prof >### Objectives > >In this lesson we will learn about inductors in order to prepare students for AC circuit analysis > > ### Theory >For the theory course, capacitors. Take advantage of the fact that the arithmetic and TC information is basically a repeat. Tie in to prior learning. >### Lab >For the lab, offer guidance on the oscilloscope. Assume students know nothing about oscilloscopes, except for the most cursory briefing in the theory class. The purpose is not to learn how to use an oscilloscope, but to show the charge and discharge of a capacitor in an RC circuit. ## Capacitance We have learned about inductors, also known as coils or chokes. We have seen that the flow of current is affected by the function of the coil. Capacitors have a different mechanism, but their properties are such that we often discuss capacitors and inductors closely together. ![[Pasted image 20210808181124.png|350]] Capacitance is the ability of a body to store electrical charge. A capacitor, sometimes called a condenser, is a device that stores electrical energy in the electric fields that exist between two conductors that are separated by an insulator, or dielectric. The principles of a capacitor are simple. Two flat metal plates face each other and are separated by an insulator. ### Units of Capacitance ![[Pasted image 20210808181554.png|350]] A capacitor's ability to store an electrical charge is measured in units called farads. One farad is the capacity required to hold one coulomb of electricity (6.28 x 1018 electrons) under a force of one volt. A single farad typically stores too many electrons for use in practical circuits so most capacitors are measured in either microfarads which are millionths (10-6) of a farad... - 1 microfarad (µF) = 1 x 10-6 farad ... or picofarads which are millionths of millionths (10-12) of a farad - 1 picofarad (pF) = 1 x 10-12 farad ### Calculating Capacitance ![[Pasted image 20210808181421.png|350]] The formula to calculate capacitance is fairly straightforward: $ C = \frac {Q}{E} $ Where: C = capacity in farads Q = charge in coulombs E = voltage in volts (V) ### How a Capacitor Works ![[Pasted image 20210808181632.png|350]] One of the plates is attached to the positive terminal of the power source and the other to the negative terminal. In this configuration, electrons are drawn from the plate attached to the positive terminal and flow to the plate attached to the negative terminal. ![[Pasted image 20210808181646.png|350]] There is no electrical current flow across the insulator, however, the plates accumulate excess electrons, resulting in the plates becoming charged. Because these excess electrons build up and stay on the plates rather than flowing, they are referred to as an electrostatic charge. The area of the capacitor that holds this charge is referred to as an electrostatic field. In fact, in the diagram above, if a voltmeter reading were to be taken across the plates, it would be exactly the same as one taken across the battery. When we looked at inductors, we considered the fact that current does not instantaneously flow, it begins at zero amps, and then climbs (rapidly) until max current is flowing. In the case of a capacitor, current flows while the plates are being charged, but stops when they become fully charged. ![[Pasted image 20210808181706.png|350]] Look at this graphic, and see the effects of adding a switch to the circuit to see two scenarios. With the switch in position A, the voltage will climb until the voltage around the capacitor is the same as the supply voltage, at which point, current flow stops. You may wonder why voltage is not being dropped over the resistor. Ohm's law explains this: Once the capacitor is fully charged, the current stops, and therefore, there is no voltage dropped over the resistor: $ V = IR $ If we now move the switch to position B, the voltage that has accumulated on the capacitor now has a path to discharge through the lamp. The lamp will briefly light up, until all of the voltage has been dissipated. If the switch is placed in its neutral position when the capacitor is charged, it remains charged until the electrons eventually leak off through the dielectric. In other words, the dielectric will eventually allow the voltage to dissipate, and the size, quality, and composition of the dielectric have an effect on how quickly. Theoretically, the charge would hold forever. In real life, not quite. ### Factors Affecting Capacitance ![[Pasted image 20210808181813.png|350]] The capacitance (capacity) is affected by three variables: - the area of the storage plates - the separation between the plates - the composition of the dielectric ![[Pasted image 20210808181848.png|350]] The larger the plates, the more electrons can be stored. One very common type of capacitor has plates made of two long strips of metal foil separated by waxed paper and rolled into a tight cylinder. This construction provides the maximum plate area for its small physical size. It also explains the shape of the actual physical device. The distance between the plates determines the strength of the electric field between them which, in turn, affects capacity. For example, if the plates are far apart, a weak electric field is produced and fewer electrons are pulled onto the negative plate. It follows then that if the plates are close together, the attraction caused by the unlike charges between the plates produces a strong electric field in the dielectric. This allows more electrons to be held on the negative plate. ![[Pasted image 20210808181949.png|350]] So, to recap, the strength of the electric field increases inversely with the separation between the plates. In other words, when the space between the plates is cut in half, the strength of the electric field doubles. However, if the space between the plates doubles, the electric field strength decreases to half its original value. Field strength vs distance is a direct inverse function, rather than an inverse square function as we saw with [[T105 Week 6#Inverse Square Law of Repulsion and Attraction|magnetism]]. This is because electric field strength is specified as a linear displacement of volts per meter rather than volts per meter squared. ### Dialectric Breakdown There is a limit to how close the plates in a capacitor can be. For example, if the plates get too close, the electric field may become so strong that electrons cross through the insulator and actually flow to the positive plate. This is known as dielectric breakdown. When this happens, the dielectric typically becomes damaged and a conductive path is set up that shorts the capacitor and makes it useless. For this reason, all capacitors are rated with regard to their working voltage, which must be at least 50% greater than the highest voltage applied in the circuit. ### DC Rating ![[Pasted image 20210808182125.png|350]] The DC rating is a measurement that indicates the strength of the dielectric (how much voltage it can handle before it breaks down). ### Dialectric Composition ![[Pasted image 20210808182202.png|350]] As listed earlier, the third factor affecting the capacity of a capacitor is the composition of the dielectric. Capacitors store energy in 2 ways. One way is through the electrostatic attraction across the dielectric. The second is through the distortion of the electron orbits of the atoms within the dielectric material. For example, as a capacitor charges, the electrons within the dielectric are attracted to the positive plate and the protons are attracted to the negative plate. This distortion, sometimes called dielectric stress, stores electrostatic charges similar to the way the plates do. ## Types of Capacitors ![[Pasted image 20210808183120.png|350]] ![[Pasted image 20210808183130.png|350]] Capacitors are divided into two types, fixed and variable. The fixed capacitors are further divided into electrolytic and non-electrolytic types. ### Electrolytic Capacitors ![[Pasted image 20210808183502.png|350]] Electrolytic capacitors are used when it is necessary to have a large amount of capacity with a relatively low working voltage. These capacitors are polarized, meaning they act as capacitors only when they are properly connected into a circuit, respecting the negative and positive leads of the capacitor. ![[Pasted image 20210808183524.png|350]] Because they are polarity sensitive, electrolytic capacitors can be used only in DC circuits. We will shortly see that AC current travels in both directions, and thus the polarity switches as the current flows. If an electrolytic capacitor is installed with the wrong polarity, current will flow through the capacitor causing it to overheat and explode. ### Non-Electrolytic (Paper) Capacitors ![[Pasted image 20210808183627.png|350]] Non electrolytic capacitors are used when relatively low values of capacitance are needed. One of the most common types of non electrolytic capacitors is the paper capacitor. The plates in a paper capacitor are made of two strips of very thin metal foil separated by a strip of waxed paper. These three strips are coiled into a tight roll, and wire leads are attached to the plates. The assembly may be encapsulated in plastic, or, as in the case of an aircraft magneto capacitor, sealed in a metal can. The capacitor shown above is what you might see in an aircraft magneto. This technique of rolling large plates to accomplish more capacitance is a common way to construct large capacitors. ### Mica Capacitors ![[Pasted image 20210808183725.png|350]] ![[Pasted image 20210808183730.png|350]] Capacitors requiring a smaller capacity but a higher working voltage are made using stacks of thin metal foil sandwiched between thin sheets of mica (a type of mineral). This stack is then encapsulated in plastic to form a rectangular block-like capacitor. ### High Voltage Capacitors ![[Pasted image 20210808183803.png|350]] For high-voltage applications, paper capacitors are enclosed in a metal container filled with an insulating oil. If a voltage surge breaks through the insulator, the oil flows in and restores its insulating characteristics. These are sometimes referred to as self healing capacitors. ### Ceramic Capacitors ![[Pasted image 20210808183837.png|350]] High-voltage, low-capacitance capacitors are made of either a disc or a tube of ceramic material plated with silver on each end to form the plates. The leads are attached to the silver, and the entire unit is covered with a protective insulation. ### Variable Capacitors ![[Pasted image 20210808183925.png|350]] As discussed earlier, a capacitor's capacity is determined by three things: - the area of the plates, - the distance between of the plates, - the type of dielectric. If you are able to change any of these factors, you can change the capacity. Many radios use a tuner that varies capacitance by changing the plate area. One set of plates, called rotors, are made of thin sheets of aluminum that are meshed together with another group of fixed plates called stators. The rotors are mounted on a rotatable shaft and the air between the plates serves as the dielectric. When the plates are fully meshed, the capacitance is at its maximum. The area of the plates is maximized, that is there is more plate area available across the dialectric. However, as the shaft is rotated, the meshed plate area decreases and the capacitance is reduced ![[Pasted image 20210808183959.png|350]] Another way to achieve variable capacitance is by changing the dielectric constant. The most common fuel quantity measuring system uses a capacitor that allows just that. The measuring units are capacitors in the form of probes in the fuel tanks ![[Pasted image 20210808184017.png|350]] Each probe is made up of two concentric tubes which fit across the tank from top to bottom. Each tube acts as one plate of the capacitor, and both the area and the separation between the plates are fixed. When the tank is empty, the dielectric is air, which has a dielectric constant of one. When the tank is full, the dielectric is the fuel, which has a dielectric constant of approximately two. The fuel indicator in the cockpit measures the capacitance of the probes and converts it into a number that reflects the amount of fuel in the tanks. ### Uses for Capacitors - Filtering - most power starts life as AC, we convert it to DC in the aircraft for our uses. Capacitors help to filter this AC current, and we will learn more about that later. - Isolation - can be used to transfer AC signals without allowing DC. This also will be covered later. - Timing - similarly to the inductors we have already looked at, there is a time element when charging a capacitor. We will cover this in this lesson. - Storage - as technology improves, capacitors are being used as storage devices in more applications. [[Capacitors as car battery|🎞]] ## Capacitors in Circuits ### Series ![[Pasted image 20210808184138.png|350]] It is often necessary to connect multiple capacitors into a circuit. When this is done, the effect is comparable to increasing the separation between the capacitor plates. In other words, a circuit's total capacitance decreases when capacitors are connected in series. Furthermore, the total capacitance will be less than that of any of the series capacitors. Is this ringing any bells for you? The formulas used for finding total capacitance in a series circuit are the same as those used for finding the total resistance in a parallel circuit. ![[Pasted image 20210808184226.png|350]] ### Parallel ![[Pasted image 20210808184300.png|350]] Connecting capacitors in parallel has the same effect as adding the areas of their plates. Therefore, the total capacitance is equivalent to the sum of the individual capacitors. ### Current/Voltage Phase Shift ![[Pasted image 20231113051302.png|350]] In a capacitive circuit when the power is added current immediately begins to flow as electrons move from the positive plate to the negative plate. However, the voltage across the plate does not immediately increase. Instead it rises as the plates become charged. This leads to what we call a current/voltage phase shift. This means that when plotted against each other, the current rises before the voltage rises. We refer to this as current leading the voltage. The importance of this will be discussed in more detail next week. To remember that current leads voltage, and to distinguish from inductive circuits which work oppositely, we recall ELI the ICE man. I _C_ E which indicates that in a capacitive circuit current leads the voltage. E _L_ I I _C_ E ### Time Constant of Capacitors ![[Pasted image 20210808184510.png|350]] Timing circuits are often made using a capacitor and a resistor in series. This type of circuit is known as an RC series circuit. The time constant of this RC circuit is the time, in seconds, required for the voltage across the capacitor to reach 63.2 % of the source voltage. The formula to find this Time Constant is: $ TC = R \times C $ Where TC = Time constant in seconds R = Resistance in ohms C = Capacitance in farads ![[Pasted image 20210808184536.png|350]] Current in the circuit will flow immediately, thus causing an increase of voltage on the capacitor plates. However, the amount of current flow is limited by the opposition caused by the resistor, resulting in a certain amount of time required to reach maximum voltage on the capacitor. The circuit will reach stability (max voltage) in 5 time constants. ![[Pasted image 20210808184714.png|350]] Time constants work the same way both directions, charging or discharging a capacitor through a resistor. This should strike you as very familiar to the Time Constant we looked at for inductors. The formula is slightly different, but the concept is similar. ## In the Lab [[T105L SAFETY|Safety Briefing]] | [[T105L WS09.pdf|Lab Worksheet]] [[What is an oscilloscope]] | [[Introduction to the Oscilloscope]] This week we will use an oscilloscope before we know very much about it. Step by step instructions and help from staff will allow us to use it to show what's happening in an RC and RL circuit. ![[Pasted image 20231107042234.png]] The first thing to get familiar with is the oscilloscope display. If you look at the graphs we used in the lesson to show time constants, this is set up the same way, that is, voltage on the vertical (Y) axis, and time on the horizontal (X) axis. The boxes, or grid pattern show measurement of these axes. These are variable, that is, the scale can be changed to suit our needs. So... ![[Pasted image 20231107043547.png]] The second thing to be aware of is the scale adjustments, the 2 knobs that adjust vertical and horizontal displays of the signal. This allows you to show the waveform in a useful way. Look closely to see that we are adjusting the volts per division or square, and seconds per division. If a waveform takes up the space of 3 squares in height, and the scale is set to 100mV, the waveform is 300mV in amplitude. Look around the display as you explore today. See what information is given and where. More to follow on this. Autoscale is your friend, and often brings the display up immediately and correctly. # Lab ## Build an RC Circuit Build the following circuit: ![[Pasted image 20221106185633.png|350]] Set up the power supplyl to provide 9VDC, 2A. Use either Ch 1 or Ch 2. Setup the oscilloscope as follows: Vertical: 5V/div Horizontal: 20 msec/div Trigger: 4.5 volts Trigger Slope: falling Probe: x10 Run/Single to Single Place the probe around the capacitor C₁. Current is measured at point A. You will be asked to hook up the waveform generator. Use these images as a reference. ![[Pasted image 20221107174531.png]] ![[Pasted image 20221107174554.png]] Waveform: Square Freq: 100 Hz Amplitude: 2 Vpp Output load: Hi-Z (press channel button to see this menu at the bottom) Output: On When using this square wave, on the oscilloscope, set run/single to run (top button)