Twenty Fourth Day

Spring 2015
28th of May's Class

We started the day learning about the AC circuit and a variant of the Voltage formula that utilizes omega, time and phi. Also learnt about the Current variant of it. Note that in this form, there is no negative value for either variable. We were also refreshed about omega, the circular velocity, which is defined by 2 * pi * frequency.

We were then taught of the existence of V(rms) and I(rms). In DC circuit, the values of voltage and current will remain constant. However in AC circuits, there is an alternating current flowing, therefore they do not remain constant, but oscillate between certain sets of values. The average value found for voltage and current values respectively is called the root mean square version of them.

As a practice, Professor Mason gave us a question regarding the voltage of the wall socket. The voltage was commonly known as being in the value of 120V. However, we were brought to the understanding that that value is actually the root mean square of voltage and not its peak, or its maximum. So to calculate the maximum voltage that the wall socket would give out, we use the formula for finding the root mean square voltage. We multiply both sides of the equation with square root of 2 to get the maximum voltage output by the socket.

Next, we experimented with a new board which already contain capacitors and resistors on it, it looked like this:

(Bordered in Green)

We used a function generator as the power supply for the circuit. Setting the frequency to 10Hz, and the voltage to 3.00V.

The set up is as shown in the drawn diagram below, with a slight error. The voltage probe should have been in parallel with the resistor.

With the probes connected to the LoggerPro, we graph out the values on the computer which looked like this:

From the graphs, we can obtain the reading of their peaks. Meaning, the V max and I max. We can also obtain the Phase Shift by finding the difference in time of the peak of current and voltage, then dividing that value by the period.

The image above is the record of the experiment we did. The maximum current and voltage were obtained by finding the peaks of their respective graphs (written in Purple). Their root mean square values are written in Orange determined by multimeter (shown below). We also derived their theoretical root mean square (written in Purple at the upper half of the white board) to compare and calculate the percent error written in Pink.

Written in Red is the formula derived for finding the Current in AC circuit as a function of time. the resulting  C * omega is the multiplication factor that differentiates the amplitude of Current and Voltage.

Although we did not take a picture of a graph created from the current and voltage, it should result in a straight line in the form of y=x. The slope generated by the graph is the Resistance of the resistor that we hooked up to the system.

This is the resultant graph when we put both Current vs. Time and  Voltage vs. Time in the same plane. They have similar shapes and movements, but they have different amplitudes and phase shifts. The phase shift can be calculated by finding the difference in the time for both graphs to reach their peaks and dividing that value by the period.

The image above shows the different variables that are frequently involved in AC circuit calculation, with an inductor present. An important variable that is introduced is 'chi', which is written in the form quite similar to an 'x'. It functions similarly to Resistance, as one of its forms is 'chi' equals to root mean square voltage divided by root mean square current. It is also the inverse of  "capacitance multiplied by angular velocity". Observing these equations, we learn that unlike capacitors, which remain unaffected when there is a change in frequency, Inductors are affected by the changes in frequency.

Next, we repeated the experiment that we did earlier. However, we do not hook it up to a resistor. Instead, we hook it up to a capacitor. The capacitor is shown in yellow box within the image below:

The image above is the record for the values we obtained from the experiment. With the same method for gathering data, the maximum for Current and Voltage is obtained from LoggerPro, while their Root Mean Square counterpart is obtained from probes. In this exercise we learnt the practical usage of finding the phase difference. It is found by looking at the time difference between the peaks of Voltage and Current, then dividing that value by the period of the wave.

Next, we repeated the experiment again, but this time it will be hooked up to an inductor (shown right below) instead of capacitor:

We tweaked a bit with the conditions of the experiment, like the voltage supply this time gives only 0.5V instead of the usual 2.0V. Chi is obtained by its simpler version, which is the Root Mean Square of Voltage divided by the Root Mean Square of the Current.

Lastly, we were introduced to the concept of Impedence, symbolized with a 'Z', much like the 'Chi' functions similarly to Resistance, the summary is in the next image:

We were supposed to have compared our finding for the experimentally determined Inductance for this inductor that we used this day. However, our data did not match our calculations from the previous lesson. This we assumed to be due to the faulty Inductor we used last lesson (which was mentioned in the previous blog entry). It might have been replaced or gave out an eccentric value, so we cannot be certain.

Twenty Third Day

Spring 2015
26th of May's Class

The class was started off with an introduction to an inductor. This is what it looked like:

As its colour is black, it blends with the tabletop which is black too. So I had it  marked in green.

Since there are a lot of information going on in the image above, I will break them down according to the colors of the boxes.

Green
This box shows the two different graphs that reflect [Induced Voltage vs.Time] at the upper half of the box, and [Current vs. Time] at the lower half of the box. One thing to note is that both of them are reaching an equilibrium value as time pass.

Red
This box contains the equation to calculate the value of a resistor's resistance using its Resistivity,  Length and Cross Sectional Area.

Yellow
This box contains the formula to find tao, which is the time constant for inductors. Which is calculated by its inductivity divided by the total resistance of its circuit.

Pink
The method that we will be using to calculate the period of the wave generated is by multiplying the time constant tao by 5. This number is derived previously.

Purple
This box shows the formula for us to calculate Inductivity, which is involved the constant 'mu' (4 * pi * 10^-7), number that the wire is coiled up, the cross sectional area of the inductor, and length of the wire within the conductor.

Next is the experiment. We were supposed to use the oscilloscope to obtain the wave emitted when a current passes through the inductor. With the frequency set at 40 kHz, and 3.00 volt supply, we obtained a graph as shown in the image above. The graph is on the screen of the oscilloscope, which is below the bluish box thingy.

The entire set up is as shown below:

The inductor is set up in a series with the resistor, and function generator, and parallel with the oscilloscope.

Using the graph from the oscilloscope, we measured with our eye power that the half time of the graph is about 4 * 10^-7 s.

Knowing the half time could get us the time constant tao, using the formula of half time divided by ln(2).

With the tao, we could calulate the Inductivity L, with the earlier formula of tao multiplied by total resistance of its path.

With the inductivity, we can calculate an estimate for the number of coils our inductor has.

However, despite the label on the inductor mentioning that the inductor is supposed to have 880 turns, our calculation only showed a meager number of 37. This can be seen as an error on the part of the inductor. From the beginning, it had been giving us problems getting the desired graph, despite our efforts in setting it up correctly.

This is the error and uncertainty that we gathered. The resistor's uncertainty was obtained from the color of its band. While the uncertainty for the time is obtained from dividing the smallest division of the time by 2.

The last part of our class involves calculation related to inductors:

The diagram in question is in the picture above, to the left side of the whiteboard.

There are 4 parts to this question.

First is Blue
We are to find the current flowing in each of the resistors in the circuit, after the switch is closed.
Since the time that the switch is closed is more than the half time, we use a special formula for calculating the current flowing in the upper most horizontal line. It is calculated as I1 in the blue box.

Second is Purple
We are to find the potential drop across both of the resistors.

Third is Green
We are to find the time taken for the voltage within the Inductor to drop to 11V after the switch is opened again. Assume that it had been fully charged prior to this.

Fourth is Black (above Purple)
This is when we are to calculate the amount of energy that the inductor release as the switch is opened.

Twenty Second Day

Spring 2015
19th of May's Class

We started the day by visiting the website: Active Physics

We were fiddling around with an applet that looked like this

To be specific, it was designed to explore the flux of electromagnetic fields. We were also given questions that are associated with the applet.

The image below is our attempt at answering each of the questions:

Basically, this portion of the class functions as an exploration into the relationship that flux of magnetic field had with the other variables. These variables include the area of the loop, its orientation relative to the magnetic field, rotational frequency of the loop.

One of the most important point to take from this portion of the lesson is that the maximum flux can be obtained when the area vector of the surface is parallel to the magnetic field vector. This is due to their relationship that is characterized by a cosine graph.

Professor Mason then conducted a demonstration using a horseshoe magnet:

This demonstration serves to prove that the right hand rule works in real life. With this arrangement, we can see that the magnetic field goes upwards, as it moves from the North to the South, and the horseshoe magnet has its South side above its North side (This was marked with a red circle). One side of the metal bar, that is marked with a yellow circle, is positively charged. The other side, which is marked with a green circle is negatively charged. Therefore this generates a current that moves from the yellow side to the green side. Causing the copper shaft to move away from the horseshoe magnet.

The current was then reversed, and this is a video of what happened:

Then, we went back to the website that we were working on earlier, and continued into another set of exploration:

The diagram this time mimics the demonstration that Professor Mason did earlier. The questions below are all related to the diagram shown in the image above.

The image right below is our attempt at answering the questions.

The exercise is still discussing about the relationship of flux to other variables. However, the variables this time are a bit different. The variables here are the magnetic field, current and electromotive force, their magnitudes and their orientations relative to each other.

The professor then introduced us to inductors. Inductors are similar to capacitors in the sense that both of them stores energy. However, capacitors store energy in an electric field while inductors store energy in magnetic field. Also, capacitors maintain a constant voltage, while inductors maintain a constant current. They function only within alternating current or voltage. As inductors uses magnetic field to store energy, its form is that of a coiled wire. Capacitors' shape is that of two plates bearing opposite charges.

The image below describes the calculation process to derive the formula for Induction.

We were then posed a question by Professor Mason. What happens to the voltage if there was to be an instantaneous jump in a circuit's current. The answer was that the voltage would leap to positive infinity instantaneously too. The image below, shows the graph related to this question marked in yellow circle. 

Then, we went back to the Active Physics website, and did another set of questions.

The questions are the same as the previous ones. It is still about flux, but with different variables. This time it has to do with Voltage, Resistance, Current, and time.

Twenty First Day

Spring 2015
14th of May's Class

Current is passed through the wire in the image above. As current flowed through the wires, the wires repelled each other. This is because of the magnetic field they produced are identical to each other. When one of the wires had its current flowing in reverse, the two wires attracted each other.

The video above shows the reaction that was described above. However, the movement from the wires are very slight.

We were asked to predict the directional vectors of the Force and Torque. The prediction we made was done in black marker. If there is an orange marker next to the prediction we made, means that that is the correct answer, and our prediction was off.

Next, we had to do an experiment related to the number of loops a wire and its effect on magnetic field. We had forgotten to take a picture of the set up so there would be no images that shows how the experiment looked like. What we had to do was coil a wire around the outer radius of a test tube. Then using a Hall-effect meter, we measure the magnetic field within the test tube.

As the coiled wire generates a circular current, the magnetic field produced would be a straight line contained within the radius of the test tube. We were supposed to measure the reading of an increasing number of loop on the test tube (From 1 to 5 loops).

The next 5 images shows the result we got, from 1 loop to 5 loops.

While it is not readily noticeable in some of these images, there is an increase in magnitude of the magnetic field, therefore it can be deduced that the strength of the magnetic field is directly proportional to the amount of loops that the current-carrying wire is coiled into.

Next, we were given two situations of a plate and the flux it experiences. As the definition for flux is the number of magnetic field lines that the surface area could enclose, the above is the resultant calculation for each plate's orientation. As the lower plate encloses none of the magnetic field lines, its flux is therefore 0.

We were then introduced to an old piece of equipment named galvanometer. Its function is to detect current and give an analogous reading.

We could not get a the earlier demonstration due to the amount of people gathering to watch the demonstration. What happened in this demonstration is basically a loop of wire is hooked up to the galvanometer, and it showed 0 A. There was no current at this point of time.

Professor Mason then took a bar of magnet and inserted it into the center of the loop of wire. The galvanometer then jumped up for a second to give a reading of Current. Then, if he pulled it out, the galvanometer would get another reading, but this time in the negative direction. He repeated the demonstration again, but this time he inserted and pulled out the magnet at higher velocity. What happens is that the galvanometer received a higher reading of the magnitude of the current flowing within the wire.

In this demonstration, we learnt of three things: Magnetic Field can generate current wirelessly, the velocity of the magnetic field determines the magnitude of current generated, and that the direction in which the magnetic field moves determine the direction of the current generated too.

Professor Mason then quickly gave us another demonstration. The red apparatus seen at the left side of the image above is a transformer. As it generates varying voltages, the current would be passed through the coils of wire in the center of the image above. The black metal pole that is seen sticking out would then generate a magnetic field.

As we can see from the video above, the metal ring levitated. This is caused by the magnetic field ,that was generated from the metal pole, inducing a magnetic field on the ring too, but in the opposite direction. When the two magnetic fields clash, they created an equilibrium of force that allowed for the ring to push itself against gravity and its mass with enough force.

In the next video, the levitation does not occur as the metal ring was not continuous all around, therefore causing current to be unable to flow through the metal ring. With the absence of a generated current within the metal ring's body, there can be no magnetic field too. Hence, there is no magnetic field that can be used to oppose the magnetic field of the black metal pole. Therefore, it cannot levitate.

The image below describes the factors that affect the magnitude of the generated current through magnetic field:

And the next image is a diagram that describes the phenomenon that I attempted to explain before about the levitation of the metal rings.

Professor Mason then gave us another demonstration about the effects of magnetic field and its induced magnetic field. He took two objects of the identical masses, with the only difference being that one of them is magnetic and one is not. He will be putting them through two different tubes. One is made of acrylic, the other, steel.

First, he placed the magnetized mass into the acrylic tube, and the non-magnetized mass into the steel tube. He let them fall, and as predicted, both of the mass fell out of their respective tubes at the same time. Next, he placed the magnetized mass into the aluminum tube, and the non-magnetized mass into the acrylic tube. This is what happened:

Basically, the magnetized mass fell through the metal tube at a slower rate than its non-magnetized counterpart. This can be explained in a similar fashion with the levitating ring. The induced magnetic field in the metal tube causes an opposition force to the fall of the magnetized mass, causing it to travel at a slower rate down the tube.

The image above is a diagram that attempts to describe the phenomenon that just happened.

We were then given these equations:

Its significance lies in the fact that if there is no velocity (stationary) from the object, there cannot be an induced magnetic field or current.