Tuesday, May 18, 2010

A Circus of Circuits

DC Circuits: 
DC stands for Direct Current because energy is supplied by the battery to fuel the dormant electrons.  These now exhilarated electrons move throughout the circuit until the battery is exhausted.  To make a circuit, it has to be closed, and by this I mean that a battery must be connected to a series of wires and resistors (such as lightbulbs) so that they form a loop for the electrons to travel.  Like the requirements for a polygon in geometry, there can be no breaks or gaps.


As you can see here, to the left, the ammeters are demonstrating the fact that in a series circuit, the current is the same at every point.  Why might that be?  Well, let's look geometrically at the circuit.  It is a closed loop, with only one path (around the circuit, from one end of the battery to the other).  Since the electrons have only one path to travel, they can't get split up (as in parallel).  So, the current remains the same everywhere because the constant flow is concentrated in only one path,    therefore it is constant on that one path.

If we look at both pictures, specifically at the voltages, we will discover something else.  The voltage of one light bulb (18.33V) is exactly one third of the voltage of the batteries (55V).  It isn't a coincidence that there are three bulbs.  What happens is this:  the voltage supplied by the batteries is split evenly among the bulbs (since they have the same resistance).  Unlike the constant flow of current, the voltage has three places to go across the circuit.  Due to the current and resistances, the amount of voltage is determined with every resistor.  This illustrates the conservation of energy (voltage).

The current is the same at every point in the circuit.  An equivalent resistance can be calculated by adding the individual resistances of all of the resistors.  The total voltage is equal to that of the battery, but can also be found by adding the voltages through each of the resistors.


Unlike the series circuit, the electrons have more paths to follow.  In fact, with the addition of every branch, there is another path for the current.  In the pictures, you will notice that the total current is 5.7A as it is coming back to the battery along the main branch.  But, when the current must choose a path, the number of electrons gets split.  Along each branch there is a current of 1.9A, of which there are three branches.  1.9 times 3 is 5.7, demonstrating the conservation of charge.  When several currents meet at a junction, their flows overlap, so in some places there could be 3.8A as well (1.9 times 2).

The voltage, on the other hand, works differently.  It is the same in every branch.  The voltage on every branch is that of the battery, 19V in this scenario.  This is due to the fact that the voltage has many paths to go across, which is the reason that it doesn't have to split.  Although that reason makes the current split, the voltage works otherwise.  Here, the voltage of every light bulb is the same, and equal to the battery.  Every bulb has its own path for the voltage to go across, thus making every branch have the same voltage.  The voltmeters in the pictures help to show this idea.

Of course, all of this depends on the resistance.  Since all of the bulbs have the same resistance, and the batteries have none, the currents are split evenly.  If the resistances changed, so would the currents although the voltages would stay the same since they don't depend on the resistance (and since if the resistance changes then so does the current, and when multiplied together, the result will always be the same).

The current is equal to the sum of the currents through each parallel branch.  An equivalent resistance can be found by taking the inverse of the sums of the inverses of the individual resistors.  The voltage is the same through every branch of the circuit.


Current works as a mixture of ideas from series and parallel here in a complex circuit.  If we recall on some ideas, we know that from series, the current is the same every where, and that from parallel, it is spilt between branches.  That is seen here.  First we must treat the entire parallel segment as one part of a series.  Then we see that the brighter bulb has 2.2A, or the total current as seen by next to the batteries.  We also see that the entire parallel segment has 2.2A, but spilt between the branches, as explained earlier.

Thus, the current acts in a predictable manner.  It is equal at every point, but under the condition that the parallel segment is considered one point.

The voltage is also another mixture.  In series, it is split amongst the resistors.  In parallel, it is evenly distributed to each branch.  To observe this, one would have to look at all four pictures.  The batteries supply a total of 33V.  Now notice that the bulb in series gets a total of 22V, not the full 33V.  Just like in series, no single bulb (if there are more than one) gets all the voltage.    Then one can notice that the other two bulbs in parallel each have 11V.  The voltage was split evenly across them, like predicted.  But why in such a complicated pattern?

After the series bulb eats away at some of the voltage, there is only the remaining left for the parallel bulbs to consume.  It is no coincidence that  33-22=11.  After using some voltage, the series bulb left some remaining voltage left for each of the parallel bulbs.  Both parallel bulbs have the same remaining voltage because they are in parallel (Read above).  In the end, you will notice that the voltage consumed by the series bulb added to the voltages consumed by either one of the parallel bulbs results in the total voltage drop of the battery.

To find the equivalent resistance, add the equivalent resistance of the parallel branches and add that to the series resistor.  The total current can be found by taking the voltage supplied by the battery and dividing that by the equivalent resistance.  To find the voltage in the series resistor,  multiply the total current by its individual resistance.  Now to find the volatge in the individual branches of the parallel part, subtract the voltage eaten by the series resistor from the total voltage.  To find the individual currents of the parallel resistors (unlike the series one, which has a current equal to the total one, as suggested by series), take the new found voltage and divide that by their individual resistances.  If you will notice, the sum of the currents that are in the parallel branch equals the total current.

I hope you enjoyed my thorough and novel-like explanation of circuits, because after all, we couldn't live the same way without them!

Monday, May 3, 2010

Waves & Optics

I learned many things during this unit, including how to ray trace and how to work with waves, including light and color.  I learned how to use the equation and thing logically about optics, when referring to lenses and mirrors.  With waves, I learned about the doppler effect and its related equation, along with sound waves.
The difficulties in my studies were with not confusing mirrors and lenses.  They also came form deciphering diagrams and general word problems, referring to frequency.  The cases of waves refracting and transmitting were also difficult to understand.
My problem-solving skills seem to be doing me good, and I have been working to my best effort on challenging problems.  I am good at ray tracing and solving equations while my weakness arises from confusion between related topics.  Mirrors and lenses confuse one another but diagrams are easily drawn.  Overall, I think that I have succeeded in this unit.

Sunday, April 25, 2010

The Science of the Eye

Because I have a passion for the brain and its mechanics, I was inspired to make a presentation about the eye, relating it to what we have just studied in physics class, and also providing some extra information.  Hopefully, this presentation is appealing to the eye, after all, it should be flattered.

The Science of the Eye

Tuesday, April 20, 2010

Contrived: Sierpinski's Reflection

            In order to produce this image, I stacked four silver Christmas ornaments on top of one another, in the form of a pyramid.  I then shone a white light through one of the gaps in the structure, which resulted in the fractal that can be seen within the ornaments, known as Sierpinski’s Triangle.  Because of the opaque and shiny surfaces, the light that I shone passed through the aperture; it is reflected back in varying colors, as seen here where the colors white, gold, and black exist harmoniously.  The gold was the result of light reflecting off of my kitchen counter, which has a sepia tone with occasional flecks of gold.  The black was due to the areas where the light didn’t reach, and serves as a good outline for the fractal.  Reflection occurs when the electrons within an object vibrate at a different frequency than that of an incoming ray of light.  The ray of light causes the electrons to vibrate briefly and with large amplitudes, which then release the energy in the form of another ray.  With this complex arrangement of spherical convex mirrors, light was bouncing to and fro, creating an infinitesimally intricate pattern.  As you can see, the fractal is formed of an infinite number of triangles, which due to the constant reflection of the four mirrors, is possible to recreate.  This image perfectly demonstrates the beauty of math blossoming in the land of physics.

If you'd like to see another picture of Sierpinski's Triangle, click here

I would like to mention that my inspiration came from 7th grade math and 9th grade geometry class!

Sunday, March 21, 2010

A Quote in the Honor of Albert Einstein!

March 14 is a day with a big significance in the scientific and mathematical world. Not only is it Pi Day, but it is also Albert Einstein's birthday. In his honor, I have picked out one of his quotes and am discussing it in the Prezi below. Happy Birthday Einstein, I hope that my analysis meets your expectations!

Albert Einstein's Quote Discussion

And in the honor of Pi day, I post a poem that will indeed say...

Roses are red, violets are blue
Pi is a number that is mighty fine
Practice often until it sticks
Practice when there's nothing else to do
Let no one ignorant of Pi enter this door
Numbers rule the Universe, I'm sure you'll agree!

Pi Day Poem: Mu Alpha Theta Shirt (2008-2009)
Million Digits of Pi: http://www.piday.org/million.php
Prezi Attributions will be found in the Prezi

Wednesday, March 10, 2010

The Physics of Short Track Speed Skating

Below is the link to my Prezi that demonstrates the Conservation of Momentum with the Winter Olympic Sport of Short Track Speed Skating. In it, you will find information about various aspects of the sport and how the Conservations of Momentum and Energy relate to it. I would like to say that I couldn't have done it without my partner, Chris, so I thank him.


Although I prefer to use the link, you can watch my Prezi below:

Thursday, February 18, 2010

Energy: It's back and its never going away!

Part A:
This unit we covered the Conservation of Energy (COE). I learned about different types of ENERGY STORAGE and how they transformed from one into another. For example, if a ball is dropped from a bridge, its potential gravitational energy disappears but is compensated with kinetic energy. There are plenty of different types of energy including the ones above, such as: chemical potential, thermal, sonic, dissipated, elastic, and internal. Internal energy usually represents DISSIPATED ENERGY DUE TO FRICTION while elastic energy comes in handy when referring to a spring or stretched cord. Dissipated energy is usually in the form of heat, as when you rub your two hands together. Internal energy remains in the system, even though, microscopically, the potential energy of the particles may change. I learned how to display the conservation of energy in Energy Flow Diagrams, so as to understand it better. I also learned about doing WORK, which is the amount of change that a force produces, and POWER, which is the rate of work. I learned how to find quantitative values by plugging them into equations involving work, kinetic energy, potential energy, and mechanical energy. With all of this newly acquired knowledge, I feel that I understand the COE much better.
This unit is definitely very difficult. There are so many options to use as equations and so many possible variables. Between work being equal to kinetic energy being equal to potential gravitational energy being equal to potential elastic energy (ONLY IN CERTAIN SITUATIONS), sometimes I don't know where to start. I draw FBDs to help aid my flaws and occasionally try every possible method as a means of getting to the answer to bypass this disadvantage.
Whether I initially know who to solve a problem or not, I always put all of my effort into solving it. My skills are efficient, and I am determined to reach the answers. My weaknesses are which method to choose while my strengths are comprehending the problems and associating them with FBDs. Some problems are more difficult than others, including ones with mu, kinematics, and circular motion. Those with springs also tend to get very tricky. I do intend on practicing what I am not good at in order to get better at them.
Part B:
Energy and everyday life are very connected. Every time we turn a doorknob or drive our car, energy is being conserved. You can see it everywhere, as when I leave the sixth story of my condo so as to reach the ground floor, in which I lose plenty of potential energy but gain kinetic energy while in the elevator. Energy is also very pertinent in biology. Mitochondria produce ATP to fuel us for the day to come. WE exhaust this energy, but it is not conserved like physical energy. What we do with the energy is conserved, like walking a long distance or hiking up a scenic mountain... or perhaps taking an elevator up this scenic mountain. Whatever we do and wherever we go, energy is present, being conserved and recycled with every step.