Vpython 2

Creating a 3D Model
We were given an assignment to code for a 3D Model, using VPython, that would give us a reading on the value of electric potential from 20 observation points, from 3 different charges. This is what our final model looked like:

We took a picture of them at different angles so that their orientation can be better understood.

This is what our coding came to be:

Within the coding, we gave the computer formula to calculate for the electric potential from each charge point and to help us also find the total, using the loop function of VPython. This is the resulting value:

Resistance

Understanding a Circuit:

A circuit is set up as below, we were asked to predict what happens when the switch is closed. Before the switch closed, the bulb marked 1 and 3 was lit and the bulb marked 2 was off when the switch was opened. After the switch is closed, nothing changed. We found iut that there is no effect on the middle path when there is a closed circuit around it. This is called short circuit.

We are then given a different setup as shown on the left bottom. 

Understanding the difference in battery and bulb system:

We make a table of what makes the difference in brightness between the bulb and the battery. When the circuit is arranged in series, the bulb is dimmer, and when it's arranged in parallel, the bulb is brighter, whereas the battery is the opposite. When the circuit is arranged in series, the battery is brighter, and when it's arranged in parallel, the battery is dimmer.

This brightness is affected by both, current and voltage. From the equation we learned before, power is current multiplied by voltage. These two gives what we know as Watt, which is the Power.

Understanding How to Read Resistor:

There are 3 or 4 lines in resistor. These lines are the color coding of how much resistance does it have. Each color has its own value. When we are reading the resistor color, first and second band are put together as the first and second number of the resistance value (sometimes third band too if the resistor has five lines), the second line from the last is the multiplier of the resistance value, so it will be 10 to the power of that color's value. The last line shows the uncertainty of that resistance in percentage.

We are then given 4 resistors and try to read each resistor value by its color coding. After doing so, we tested their resistence with the multimeter.

The first resistor, by color coding is found to be 1200 ohm with uncertainty of  5% and was tested to be 1256, which was in the range of the uncertainty, so this was correct. The second resistor, by color coding is found to be 20 x 10 ohm with uncertainty of  5% and was tested to be 198.6, which was in the range of the uncertainty, so this was correct. The third resistor, by color coding is found to be 30 x 10^2 ohm with uncertainty of  5% and was tested to be 3060, which was in the range of the uncertainty, so this was correct. The forth resistor, by color coding is found to be 33 ohm with uncertainty of  5% and was tested to be 40.8, This was slightly off because it was not in the range of the uncertainty. This may be due to ...

Using multimeter to find resistance:

Given 3 resistors, we want to set it up in different arrangements. First, we want to find the resistance of 1 resistor, which is foun to be 612 ohm. Then, we want to attach another resistor next to it and find the resistance of both to be 1225 ohm. Attaching another resistor, we found the resistance to be 1835 ohm.

Next, we want to take them all apart and attach one of the resistor on top of the first one instead of next to it and find the resistance using multimeter. When we place the multimeter needle in between the two resistors, we found the resistance to be 306 ohm. Then, we add more resistor parallel to the two resistors. We found the resistance to be 204 ohm.

From these data, we can conclude that in series, the resistances are added, whereas in parallel, the resistances are divided depending on how many resistors there are.

Understanding Equation of Resistance:

When in parallel, the equation of resistance will be 1/Req=1/R1+ 1/R2. When in series, the equation of resistance will be the sum of all resistance.

Given the mixture of parallel and series in a circuit as below, we have to separate each of them. Start by adding the series first. The top series resistance will give the sum of both, which results in 320 ohm. Then calculate the parallel of that part, this gives about 76 ohm. Then add it with the series next to it, which results in about 176 ohm. Then we calculate the bottom parallel, which gives the out resistance to be 110 ohm. The last resistance is in parallel. Using the parallel equation, we found the final resistance to be about 70 ohm.

Understanding Kirchoff's Law:

Components in Electricity

Understanding charges in 2-D:

We have learned a lot about voltage in the past. Voltage is electric force multiplied by distance, which is also k multiplied by charge and divided by radius squared when the charge is in a straight line. Today, we are learning about the charges when it has a component on it. To find the radius, we can use pythagorean theorem. The equation of this radius can be substituted into the equation of the voltage when the radius is unknown. First, we are integrating in respect to r, then we found the equation to be k multiplied by charge divided by the radius. The radius is substituted with the sqrt(x(square) + a(square). From that, we find the equation as below.

The electric force itself can have component.

We are now given a ring with 20 point charges acring on a single point. The point is at a distance 20cm away from the center of the ring, and the radius of ring is 30 cm. We can calculate this by hand, which will be using equation of voltage as kq/sqrt(radius(square)+x(square)). By plugging in the known, we find the voltage to be 4.99x 10(5) as below.

We can also use spreadsheet to calculate the total voltage. We set the known in for radius, x, charge, and constant as below. Then we set the equation to be ... For 20 points. Then we add all of the voltages and found the answer to be the same as done by hand.

In the spreadsheet, we recorded the x and y-axis. Y is the same for every point of x, but x changes every 0.01 since we will split it up into 16 parts. K is always the same and charge is also given. We wanna calculate r first which equation would be ... And also set equation of voltage to be. Finally, we will sum all the voltages to find the V total as below.

A rod with length of 0.16m with charges that is located at (0.1,0.15) is given. We want to find the total voltage at the rod. If we split the rod into 16 parts, doing the calculation by hand would be tidious; thus, we use spreadsheet to calculate them.

We also find the relationship between k, lamda, q, a, x, and b. We know that the volte is integration of k

Voltage, temperature, potential energy, and work in electricity

Understanding battery system:

We started the day doing an experiment on lightbulb and battery again. First, we connect 1 battery to two bulbs and see how the bulbs light. Then, we connect two battery side by side to 1 lightbulb and see how the bulb lights.

The brightness of both trials are equal.

The bulb thats connected to batteries that are side by side is dimmer than when the batteries are stacked up because when the batteries are stacked up, the voltage of both batteries are added, whereas when the batteries are side by side, is the same as using 1 battery voltage. Because of this, using 2 batteries or 1 battery earlier give the same brightness result.

When drawn in a circuit form, there are parts on the circuit that can be drawn to indicate each, which are battery, resistor, bulb, and switch as shown below. 

Understanding relationship between voltage and temperature:

The next experiment is water heater. The Water heater is powered by battery.

The graph below shows the 2 minutes that it is heated.

Then, the voltage is doubled and graphed for the next 2 minutes as shown below. When the voltage is doubled, the scalar factor is multiplied by 4, theoretically because the current is squared in temperature. Thus, the slope is steeper.

Understanding work in electricity:

There are 3 paths that can be taken to move on a slope. Going parallel to the charge then perpendicular, going perpendicular to the charge then parallel, or just going parallel to the slope. We wanted to see the difference in work on each path. Work on a path that's perpendicular to the current is 0. Thus, we only count the work thats parallel to the current. After doing the calculation, the total work for all path turn out to be equal.

When given a current and 3 different ... On it, we want to rank them from the least work to the biggest work. The work perpendicular to the current is zero as we learned because the angle between the current and the .. Is cos 90*, which is zero. This makes the work also becomes zero. The next one would be the .. Slanted to the current, then the ... Parallel to the current as calculated below.

Recall from past lecture, that Electric force is equal to charge multiplied by electric field; then, we can substitute force with them as well.

Understanding potential energy and work:

We now learn that potential energy in electric is equal opposite to work. But we know that work is force times distance, which force is also charge times electric field; therefore, work is integration of charge multiplied by electric field and change in distance. We also know that voltage is work per charge. By equating these equations, we can find the voltage to be integration of electric field multiplied by distance.

Vpython:

Given program as below, we have to predict how it would look in the whiteboard.

We predicted the 2 charges to be on the x-axis, one one (-2,0,0), and the other on (2,0,0). We also predicted the observation point on (-1,0,0).

After making the prediction, we calculate the V total using the given charges in the program, which are (-1 x 10(-9)) and (1 x 10(-9)). We also use the distance from each charges to the observation point. Using this known, we plug it in to the formula of voltage that we have known from earlier, which is kq/r, and add the voltage from both charges. We found the total voltage to be -6V. When the observation point is moved to (1,0,0), we can use the same method and found the voltage to be 6V.

When we run the program in vpython, the screen shows as below, which followed what we predicted.

The next blog will show vpython that we are assigned to do and we are allowed to work together, but we have to remember, "collaborating, not plagiarizing"! :)

~THE END~

Gauss' Law

Understanding Gauss' Law:

We started the day understanding about the relationships between charges and electric field. Given 3 charges at different locations, the electric field is shown as below. We also learn about the relationship between flux and charges. When we try it in the website written below, we found that as charge increases, flux also increases. This means that flux and charge are proportional. Lastly, we learned about gauss' law, which says that flux is equals to integration of Electric field multiplied by change of Area.

Faraday Cage:

Electric from the ... Is connected through a metal conductor to a faraday cage. This experiment is to show the location of the charges around the faraday cage.

Given a situation where there's a lightning storm when we are stuck in a car, we needed to find the best decision to make to avoid this lightning. Staying in the car would be the best decision because lightning would hit the metal first and the metal would be grounded.

There are strings hanging on the inside and outside of the faraday cage. We want to know where the charges are located on the faraday cage. When we activated the apparatus, only the strings on the outside are moving. This shows that the charges are only on the putside of the faraday cage.

We learned from earlier about gauss' law.  We also know that flux is charge divided by ... By equating these equations, we found that integration of electric field multiplied by change in area is equals to charge divided by ..

By using the equated equation, we cab now find the equation of electric field by itself by dividing both sides by Area, but we know that charge divided by area is sigma. Therefore, the equation of electric field is sigma divided by .., which can also tell us the equation of sigma.

The way that faraday cage works is that charges wants be at the maximum distance of each other. The maximum it can be in a faraday cage is in the most outer part of the cage. Thus, there is no charge in the inner part.

Battery system, electroscope, and multimeter

Understanding the mechanics of battery:

We are given a battery, a lightbulb, and a wire. We needed to find 2 ways that will make the lightbulb light up. One of the ways is by putting 1 end of the wire to the negative end of the battery, and the other end of wire to the body sides while placing the bottom side of the lightbulb to the positive end of the battery. Another way can be by switching the position of the bulb and the wire. By placing the bulb horizontally and let the sides touch the positive end of the battery, we can light it up by placing the wire on the bottom of the bulb. Both of these position works, as long as we place the wire and battery on the conducting part of the bulb, which are the metal sides and the bottom of the bulb. When we add another battery, we can stack up the battery alternatingly, and place the wire the same way we did before, the bulb will light up brighter. This happens because of the greater energy put into the bulb from the battery.

Electroscope:

We are introduced to electroscope. This apparatus is used to see the presence of charge and the magnitude of the charge. We took an iron rod and rubbed it against pelt to accumulate charges. Then place it on the conductor. The 2 films then repell. This proves that there is a charge on the iron rod.

When we placed battery on the conductor, the 2 films did not repell because battery has 2 poles, which needs to be a closed circuit for it to work. There is only an inlet from the conductor; thus, battery would not work with this electroscope.

Understanding Battery Contents:

Energy as we knew from 4A is capacity to do work. A battery contains energy that can be used to make a bulb light up. Using 2 wires, from the positive side, we connect it to the sides of the bulb. This wire lets the positive charge flow to the bulb. The second wire brings the charge to flow from the bulb to the negative end of the battery, making it a closed circuit.

Electricity depends on height ans flow rate. The height is known as voltage, whereas the flow rate is current. 1 Voltage is equal to 1 joule/column, which relates to energy per charge in a circuit. Current is charges per time, which in units will be column/sec, which is also equal to 1 ampere, but power we know to be energy per time. By equating the voltage and current to power by their units, we found their relationship to be P=I*V

Amperemeter:

Using this apparatus, we can find the current flow of each wire. By ataching bulb to the battery as we've done couple of times, we attached 2 more wires, from the negative pole of the battery to the positive screw on the ampere, and another from positive pole of the battery to 150 screw on the ampere. We found them to be about equal to each other.

When the two wires are attached to a lightbulb and the charges flow through the wire, we wanted to know whether the current before and after it passes through the lightbulb is the same or not. We can find out using the amperemeter.

Given 1.5V, 120 mA in a closed circuit, we want to find how much power is in the system. Using the relationship of power, voltage, and current, we can multiply them to find power as below.

Drift Velocity:

We learn that we can find current flow by multiplying density, charge, drift velocity, and area perpendicular to flow. This is known as ohm's law.

We now want to find the relationship between voltage and current. By using ... We proved that Current and voltage are proportional to each other; thus, using calculus, we found the slope to be derivative of V divided by derivative of I.

Understanding of Resistance:

We learned the relationship between resistance, voltage, and current. Resistance is voltage per current. By substituting them with their units, we found the units of resistance to be kg*m/s*C(square).

We also wanted to find the relationship between resistance and length. Using multimeter, we found that the longer the rod, the higher the resistance. And the larger the diameter, the smaller the resistance. Therefore, we learned that the equation of resistance to be resistivity*length per Area.

Multimeter:

Using this apparatus, we can find multiple things, voltage, current, and resistance. We simply take an iron rod and place the connector on the rod. We then ..

Understanding Resistivity:

We qucikly learned about resistivity. Resistivity is proportional to temperature because of more collision and it's also proportional to amplitude, but it is inversely proportional to free path of electron.
We also learned about the relationship between resistance and temperature. Change in resistance is proportional to change in temperature. The equation is as shown below. Change in resistance divided by resistance initial is equals to its temperature coefficient times change in temperature.