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.