RL&RC Circuits and Inductors

This lab had the intention to explain to students what an inductor is, does, and how it can be calculated. It also explains the relationship between the resistors and capacitors in a circuit.

RL means that a circuit contain a Resistor and an Inductor that are connected in series or can be connected in parallel. The Resistor has the function to reduce in certain way the amount of current that can pass. This finality has different applications, where one of them is the water portable immersion heater. Since the current that passes through it is at higher values, the resistance that is presented will limited how much passes and that will create some heat that is released to boil water or a liquid. However, the Inductor acts like a "police border". If a circuit the current that passes through it is increasing, the Inductor will "put the current in waiting". This will create a back EMF some of the energy from th current will be storage and it will create a magnetic field. This works accordingly with the Lenz's. When the current within the circuit increases a back EMF, when the current decreases the EMF goes in the same direction as the current. And when the current is decreasing, the inductor will supply the circuit or act like a battery. The energy that was stored in the magnetic field will be converted in a potential voltage, supplying the circuit with additional current flow.

The picture above, related the Gauss's Law for Magnetism and Faraday's Law for Induction to find the mathematical expression for the induction, represented with the letter L and with Henries (H) as its unit. We can see from the picture that L is always positive, even with the EMF being negative.

In this two pictures we can see that a inductor and a resistance connected within the same circuit. The resistance can be found in series or in parallel, but an inductor is found connected in series with a resistance or capacitor. For a RL circuit, a circuit with a resistance and an inductor, the current is the one that will determine how they will behave. For example, if the current through the circuit is constant the inductor will act as a wire, that means that we considered that there is no changing in direction for the current, except the amount of current that passes through since a resistance is present.  It is also importante to know that, the EMF can be either positive or negative. It will be negative when a back EMF is created that is when the increasing current is passing through the inductor. And it will be positive when the current that passes through the inductor in decreasing. 

Frequency Corrector

The photos below are representing a oscilloscope that was build to correct signals and diminish the noise, related with frequency, inside of an electronic apparatus. The idea is that a magnetic field is applied to the current that passes to the reading channel, the black object that looks like a flashlight, and corrects the possible deviation that the signal may bring from the source. It also can be use by professionals, like electronic engineers or sound engineers, to understand what is going on inside of a device and make possible to explain any anomaly that is happening. The last photo represents the electronic oscilloscope, and the first photos is the more "rudimentary" one.    

In this photo students were trying to work or understand how to make different sounds using an oscilloscope. By increasing the frequency, they could hear a higher pitch; and by decreasing the frequency, a lower pitch could be heard. For example, for the triangle wave, the vibrations would be lower than the ones produced by the sine wave; likewise, the square wave produced a lower vibration. They also saw that by changing the amplitude of the waves, the sound would changing also. This is because it can take less or more time traveling from one side to another. A lower one would take more time, since the space between the waves would increase, and a higher one would take less time because the space between them would decrease. 

Magnetic Field

This lab student were trying to understand how a magnetic field works. 

In this photo we can see that the magnetic field travels from South to North; if we look at one battery, we can see that the South pole would be the positive terminal, and the North would be the negative terminal.  

In this photo we can see that how it the magnetic field flows. Although the picture shows from North to South, actually it works the other way around. As the calculated the flux for the electric field, here we can also calculate the flux for the magnetic field, where indeed is equal to zero because what goes out, must come in. 

We also found that force on a magnetic field is calculated using the crux product in which the charge (B) is perpendicular to a constant K and the electric potential of the system; and as we can see it, the force acting on an electron, is always perpendicular to the direction where the electron is moving. The photo also gives information that the work done on a close loop will always be zero because the electron will return to its initial point. It can be seen as being the same as saying that the particle has never abandon its place.   

This photo shows that the velocity can be calculated in terms of angular velocity. And the force can be found using the intensity and the length in which the electron has follow. Applying the differential equation in both sides, we can see that the charge is constant as well as the intensity. But the force and the length will always change because the electron will never be in at the same distance throughout its travel within the magnetic field. 

Capatitours

This lab students had been testing capacitors and try to understand their usage. A capacitor, also known as condenser, is a electrical component that has the ability to store energy, electrostatic energy. Capacitors are presented in various forms and sizes where the capacity of storing energy also varies with the size of it.

This photo shows the relationship between capacitors in parallel and in series. Comparing with a resistance, capacitors are calculated differently when they are in parallel; in this case, the total energy storage on a capacitor is the sum of the all the energy storage on each capacitor within the circuit. Whereas, the total energy storage on a circuit that is in parallel, is the inverse sum of the individuals capacitors within the circuit. 

In a parallel or series circuit, we don't have intensity, but  charge, since a capacitor is storage device in a circuit. With a parallel circuit, the total electric potential is equal throughout the circuit, and the total charge, is the sum of the individuals charges from each capacitor. In a circuit that is presented in series, the total the electric potential is the sum of the individuals electric potential on each capacitor, and the total charge is the same the each capacitor can storage.    

The first photo represents how a capacitor behaves when it is been charged or discharged. the lower photo, at the upper right side, are the graphs that represent each one. The bottom graph represent the capacitor being discharge, the line going down, or charge, the line going up. The top graph represents the intensity of the capacitor. Notes that even being charging or discharging, the intensity becomes stay steady after a a while. This is because the electric potential will also be constant because it reaches its maximum or zero electric potential charge.

 

Resistance, Parallel and Series Connections.

This Lab had the intention to demonstrate what happen when we add a resistance to a circuit or we can say to see to effect of a resistance on a circuit. It also students saw or were get an explanation about a circuit in series or parallel, and how to calculate the intensity and voltage.

This photo was a prediction to see what could happen with the lamps if they would light or not. Will light if the switch if on; but if it is off, electrons cannot flow or pass where we connected the switch and the bulb cannot light. The next two photos will demonstrate the opposite because we demonstrated the opposite of our prediction. 

The first photo shows a simple circuit that is connected in series if we see the top loop or the bottom one; but if we see it as one, we found that the two outer bulbs are in series and the third one is in parallel with those two. Although we do not see any resistance, the bulb itself has a filament that has some resistance to delay the passage of electrons, causing a light that we all use at home. 

The second photo, we did not use bulbs, but batteries either in series and parallel. 

This photo illustrated what was announced at the beginning. The top circuit is parallelly connected, and in such case, the sum of the voltage that passes through the resistance, independently of how many we have, is the same as the source voltage. In series, we found that the intensity will be the same, independently of how many resistances we have on the circuit.  

Potential Energy (Voltage) and Charge Relationship.

Where we will post some relations between Voltage and the Charge on an electron or proton, since are the ones that we, students, use to make our calculations.

In this photo a relationship between voltage and the charge that a rod. If we have a point charge passing near the rod, it will experience a charge the is presented throughout the rod length. We must remember that the charge is not the only one that will make the voltage increase or decrease; indeed, the charge is constant, but the parameter that influences the change in the voltage is the Radius. And the relationship is as flows; bigger the radius, using the same charge and knowing that the K is also constant, small the voltage that the point charge will experience. On the other end, smaller the radius, and keeping the same constants charge and k, the bigger the voltage that the point charge will experience. However, there is a maximum value that can be experienced by the point charge which is when the distance between the rod and the point charge has an angle of 90 degrees. And the minimum value would be when the radius goes to infinity, and in this case the voltage would go to 0 Volts.     

This graph represents a lab done to see the measurements of various points using a power supply. The shows a peak of a maximum value for the voltage, and that is when the distance between the point charge and the device that we were measured the Electric Potential was the minimum on that particular experiment. Even though we had predicted that bigger the radius, smaller the voltage or the electric potential, in this experience we saw that after passing the point where the electric potential has its maximum, it keeps constant as we can see in the graph. I may conclude that accordingly with the distance, the ratio (charge/radius) will keep constant until it goes to zero. 

For this photo, the first one, we found a relationship between a disk and a point charge around of the disk's surface. Although the direction of the charge, or where she will move, changes accordingly of which part of the disk is being used to calculate the electric potential on the point charge. The second one, shows that the electrical potential is equal independently of the piece we choose to calculate the voltage on the point charge. 

Here we could relate the electric potential and the work done on the point charge. Yet, the charge value used can be different or even the same. For example, if want to find the work that one particle that is charged does on other particle, we have to have the or calculate the electric potential of both particles or the one that is missing. This result will tell us how strong or weak one is relatively to the other.  

 

Work, Voltage, and Energy relationship

Energy work theorem it is also applied to in the current analyses. As seen in class, work does not depend which path the study object takes to find the amount of work done during that trajectory. It depends just on its initial and final position.

In this picture we have a point charge with various options or possibles directions that can do work. Work is define as the charge that a particular has times the difference in the potential energy or voltage that flow throughout the system. And since the difference in voltage is calculated using the integral because is not the same since a portion is transformed in light, work will be the integral of charge times the electric charge times the distance in which the point charge is moving and the angle it does. From this picture, we can see that the point charge will move in the same direction as the electrical field, but it can move in both directions and produces a negative or positive work. in this case our angle will be 0 degrees, which is A direction.

 As cosine increases the work done on the point charge decreases, which makes sense because it becomes more complicate 'break' the electrical field or the natural flow of the electrical field. As the particle changes its motion tendence and reaches the points D and C, the work is zero because the angle and is zero. Indeed, at this two points, it becomes complicate to move the point charge side way because would require the work to be infinitesimal huge to pass through the electrical field and interrupt the electrical flow. 

This picture simple shows that the electric field moves accordingly with the shape of the surface where the charge is inserted, or where the charge is place. For example the surface can be a cylindrical surface and the electric field will be flown in all directions. 

       

Voltage, Resistence, and Current.

During this lab, we were analysing how a circuit would be functioning. The picture describes at least four ways that a bulb could be lighted. In all the possibilities, the current flows normally, from the negative to positive, which is the way that must be done so humans can have lighting at home or office. The third scheme, at bottom from left to right, the bulb cannot be lighted because there is not current flow and the the potential difference between the negative side and the positive side cannot be verified. In this case the current will accumulate and there will be an increasing in the temperature. In a home circuit, this temperature rising would, probably, cause a short in the electrical circuit.

This picture gives in a few words how the a simple electrical circuits works, and it is like the one described above. The battery gives energy, the filaments at the bulb will resist to this flow and at same point it will produces light; after passing this resistance, the current will flow back to the battery and the cycle starts all over again. fro this to happen, electrons must flow from one side to another. And for this to a continuous flow, it must have in the circuit a potential difference that is verified when energy tries to pass through the bulb's filament. 

This picture shows that bigger in diameter a wire is, less resistance it will be presented. Lets use an analogous example. When we have a water pipe coming from a water facility treatment plant, it will be divided in various others pipes to reach each of our homes. But lets keep with three just. From the main pipe, we see it that has also two other pipes, one with a bigger diameter than the other one. Water, as humans, will choose the way with least resistance to make the water flow normally and do not cause major problems in the pumps. The same analogy is applied to wire and current flow.

This photo represents a simple circuit where the we have a battery, cables to make the current travel from the positive to the negative pole of the battery. In addition to the lam and battery, a voltmeter and a switch are also included to open or close, making possible that current can flow or not from one side to another. The voltmeter is the controler, like a border, that controls how much is traveling throughout the circuit. 

  

Flux (Continuation)

 Like the last post, in this one we still discussing flux.

  In this photo, students were analysing the lines between three charges and within close, chosen, 'surfaces'. The surfaces that have the point charges within their boundaries will some charge that will go from one point charge to another. It means that they have 'electrons circulating even at the border. Those surfaces are S1, S2, and S3. The Surface S4 has zero flux, because no charge is inside of its boundaries; even though it has a line that passes through, it does not count as as electrical circulation.

In this picture, we had to find a explanation from flux and a mathematical expression that could describe the flux inside of a surface area in a given volume. And since the volume can have any shape, we perform that calculation using integrals. 

This two pictures are describing what happens when a compact disc is putting inside of a micro-have. Lets use water as an example. To heat water, microwave have to 'shoot' electrons that will 'excited' the molecules of water. As the molecules starting get more excited, they will start to gain heat. At a certain point, the molecules will starting to separate from each other, and the water will start to boil. However, with objects like a compact disc, the response is quite different. Until one point it will receive the charges that the microwave will send to heat the disc. But after being saturate with charges, it will re-send it back, or reject, because it cannot expand. At this point the only solution will be 'exploding' to release the excess of electrical charge. The last picture shows what happens when the disc had reached its 'saturation' point. The link bellow shows what we describe it what happens when a compact disc is getting harm on a microwave. 

 What happens with the disc

Electric Flux

In this lab, students were presented with a new concept called Electric Flux (E. F.). E. F. is physically defined as the measure of the number of electric field lines that pass through a surface. One thing that must be said is that EF is always perpendicular to the surface that is been study. 

 This picture represents a prediction that students did of what could be the behavior of a point charge that had been shot and had to pass to an electric field. The prediction was to see where the point charge would go. As the picture shows, the point charge moved to the positive charge, and this movement is described by the moment of Inertia of a particular, which describes how easy or difficult is to a particular move. However, the definition of inertia is that an object tend to remain in constant movement or stopped if there is not external force that change its initial situation. 

In this picture, how to point charges would behave if they were placed in the center of an electric field with some E. F. The conclusion was that the electric field produces a force on each charge, making both of them rotated and keeping the distance between them equal. Since this movement is a rotational movement, the mathematical expression to describe it is Torque (represented with the Greek letter tau) which is described as a force that is applied to an 'object' at certain distance from its point of rotation, And must be always perpendicular to its point of rotation. 

Faraday's Cage

The first picture are just pure calculations in where students could find a mathematical expression to calculate the word done by a point charge. 

The second picture describes how the Flux works on a surface. As explained before, it is always parallel to the surface of the object in study. The video can give us an idea of how this works, even though we do not see the electric field on the Cage. 

Flux Video

In this picture, the intention is to demonstrate that accordentely with the angle between the electric field and the an area enclose withing the direction of the flux. Since the flux is related with the function cosine, it can be said that by increasing the angle between the flux and its direction, we will have less electric field  or lines inside the imaginary 'circuit' created to calculate what can be asked, such as the Flux.  

Electric Field

 Electric Field

The aim in this lab was to show how electric field works and how it can be applied to human being daily live.

In this picture, students were asked to present some concepts about the electric field by using the ideas or the knowledge they have about gravity. Here are some taking from the picture:

1. the electric field is is caused by a charge of some object, like proton or electron. 
2. the magnitude of the electric field depends on the magnitude of the charge that produces the field. 

Likewise, gravity also affect any object, because every object has mass and is affected by gravity that pulls things and avoid them to 'travel' throughout the planet or 'galaxy'

In this picture the students analyzed the forces produced by one charge into another. And the final thoughts, resuming, was that when q1 is near the q2 the field becomes bigger, and father it is, the electric field creases exponentially.  In fact, by keeping the force constant and make the charge varying, the electric field will increase when the the charge is small, and decrease when the charge is bigger. This can be viewed by using the mathematical formula E=F/Q. E (electric field), F (force), and Q (charge). 

 The first picture represents the relationship between the electric field and the force. Either one E=F/Q or E=kq/(r^2) will give the same answer. Nonetheless, all depend what information is convey on a problem.
The second picture is the continuation of the second picture. The conclusions are that the force experienced by a charge remains the same, but the charge itself change sign. The formula F=qE is connected with this result.

In this picture the intention is to see what happen when two objects with the same charge get near each other. For example, when a circular or spherical object has a negative charge and we pass a charged rod with also a negative charge, the charge on the rounded object will spread equally throughout it, making equal angles between them. Numerically speaking, the electric field depends also on the distance between the fixed point and the object that is charged passes near the fixed point. For example, calculating the electric field from a fixed point to a rod with 10 cm in length, we will find that when we get near the center, the electric field is smaller than the one at the beginning of the rod. As stated previously, and like the force, the electric field also depends on the distance between the two charged objects; bigger the distance smaller the electric field.

This worksheet describes the experience made by students in where by increasing the radius between the charges either one the force and the electric field will vary accordingly with the distance. 

Here is a demonstration in how the electric field can be calculated when the charges are not directly pointing to the fixed charge. To a more accurate calculations, the electric field is calculating using the x-axis and y-axis so the direction and the magnitude of it can be determined easily, and are given in terms of vector notation.  

    

Electrical Forces

Electrical Forces

This lab had the intention to show to the students how the electrical forces can work by using material that we are in contact with on daily basis.

Our physics professor Dr. Mason started the lesson rubbing cat hair and a balloon to see what happens when the glass and the balloon are in contact (first picture). By rubbing this two materials, electrons will be transferred from one to another, causing the balloon to increase its electrical charges. When the balloon was placed near the glass they sticked together as they were glued. This happens because each one presents different chargers when in contact. The balloon may have negative and the glass positive charge, or the glass may have negative and the balloon positive charge. In fact, if they both would have the same charge, positive or negative, they would not be sticked because same charge always repels each other. 

In the second photo, a silk was used to see if the balloon and the glass would behave in the same way. Although the rubbing object used was different the effect was the same. This two experiences had shown that no matter how a person may rub a balloon, or other mass the can gain electrical charge, it will always generate an electrical charge in such away that when placed near a mass with an opposite charge they will stick together. 

The third photo explains what happens in both experiences, on the left side of the last photo is a free body diagram which represents the forces acting on the balloon and the contact force. On Y-axis: Force due to gravity (+Fg, taking the positive down) and Friccion (-Fr, because it goes in the opposite direction of the Fg), and on X-axis: Force that the balloon does on the glass (Fb) and the force that the glass does on the balloon (-Fg, or normal force). The forces in the X-axis are equal in magnitude but opposite in direction, so when added the net force is zero. And that is the reason why the balloon and the glass in both cases can stick together. 

Aclaration: Even Though the red balloon is sticked to the wall, initially it was with the glass. The intention was to show that two methods were used, and they had the same effect.

After doing the practical learning, student went to the theoretical learning which consist in try to find a definition for electrical charges. And at the end, the simple definition that was found is: Charge is how much matter interacts with other matter electrically.

After the definition, students had to perform a experience with tape. Four strips of tape were used, and each one was labeled. Two were written of top and the other two bottom. They had to induce some charge on each of it by sticked them on the table and pulled. After that, they had to three different combinations, such as, top and top, bottom and bottom, and top and bottom. The conclusions were: when the two tops were placed together, they would repeal each other because the have the same electrical charges. The same happened when the bottom were placed together. When top and bottom were placed together, they sticked since they had different electrical charges.

The first photo represents the derivation of the force used to calculate the electrical forces when one mass is approaching another one with the same electrical charge, and the second one starts to repel the first one. 

The second and the third pictures are simple calculations and the answers for the questions on the lab. 

Those formulas are also known as the Coulomb's Law, which mathematically says that the force of the electrical interaction between too chargers depends how apart they are from each other. Bigger the distance, smaller the force. And the most important of all, the distance cannot be zero, otherwise the force would be infinity.