Electric Circuits, Work, Electric Potential, and VPython Simulations (4/14/2015)

Circuit Diagrams

The configuration used to simultaneously
light both bulbs as brightly as possible.

The configuration used to simultaneously
light both bulbs as dimly as possible.

To start the day, we were asked to create a circuit which caused two bulbs to light as brightly and as dimly as possible. Once we physically created those circuits, we drew them on the whiteboards as seen in the first pair of drawings above. Afterwards, we were shown what the proper circuit symbols are, and redrew our circuits in the proper format. The bulbs are shown as double loops, and the batteries are shown as a pair of bars (one shorter and one longer, symbolizing the positive and negative sides). It should be noted that in the "Bright" circuit, the layout of the batteries is referred to as "in series".

Power in Electric Circuits

A power supply connected to a heater and logger pro in order to gather data. 

For this experiment, we were asked what three factors we need in order to figure out what the temperature change for the water would be after heating it for 2 minutes. We were also asked what would happen to the change in temperature after the voltage was doubled. Our answers are shown above, but it should be noted that our answer for the second question is incorrect. The temperature DOES NOT increase by a factor of 2.

Shown above is the data gathered from two minutes of heating at an initial voltage, and then at double the voltage. As you can see, the increase in temperature is much more than double. The temperature change actually increased by a factor of 4. The reason for this is because if you evaluate the equation Power = Voltage * Current, and multiply Power by 2, you see that the equation becomes 2P= 2V*2I. It then becomes 2P= 4*V*I, and it becomes obvious that the factor that temperature will change by is 4.

Electric Shock Hazard

We learned that if a person is struck with a voltage of 120V (2.4W/20mA), death will occur in several minutes due to breathing having stopped (by way of paralysis of the chest muscles). We calculated how much current would be flowing through a person by using the average resistance, R, of the human body, 1 mega-Ohm. The result is that a current of 1.2*10^-4 C/S

Work in a Gravitational Field

In order to analyze how work operates in a gravitational field, we were given a situation where a cart starts at point A, and evaluated three paths to get to C. (Ignore the a>c>b notation. That comes into play in the next section.)

As seen in the calculations, the work along all three paths (A->C, A->B->C, A->D->C) is identical. Therefore, work in a gravitational field is path independent in situations such as these (where all paths start and end at the same point).

Work and the Electric Field

In this example, we are given three different paths of equal length in a gravitational field in which a charge of q travels, and we are asked to rank them in terms of most to least work done.

Our prediction is that path A results in the most work, path C in less, and path B produces the least amount of work.

After some quick calculations, our predictions are shown as correct. Path B produces zero work because the height never changes. Path C produces less than A because the range of cos(theta) is (-1,1), and those values can only be reached at angles of 0 or 180 degrees. Since C contains an angle in between those values, when you multiply cos(theta) into q*E it will lower the entire value, when compared to path A which is simply q*E.

Electric Potential Difference

Electric potential difference is defined as the work per unit charge that an external agent must perform to move a test charge from A to B without changing its kinetic energy. From there we can conclude that the units for potential difference is Joules/Coulomb, and we know that 1 J/C = 1 Volt. This explains why potential difference is referred to as voltage. So in order to calculate how much voltage is needed to move a charge from point A to B in an electrical field, we formulated the equation above. A and B are the points, E is the electrical field, and ds is the measure of distance between the two points. 

Connection Between Electric Potential and the Electric Field

Electric field lines are always perpendicular to equal potential lines. In the photo above, the crossing lines are considered the electric field lines, and we have drawn a circle depicting the equal potential line, which is perpendicular to every electric field line.

The Potential Difference for a Point Charge

We are asked to show that if A is at infinity and B is a distance r from a point charge q, that the potential V will be given by the expression V = k_eq/r. That is what is shown in the calculations above, which represents the equation needed to find the potential difference for a point charge.

VPython: Electric Potential

Before simulating electric potential around charges in VPython, we were asked to manually calculate the potentials of two point charges located between the electric fields. It turns out that the two test charges are of equal and opposite magnitude, due to their identical distance between each other and the q charges.

After running the original simulation in VPython (the sim that we calculated the correct electric potential of), we were asked to add an additional charge (located in the negative y axis). Once that charge was placed, we needed to calculate the net electric potential of these charges at three different points. We simply added three more points (on the positive x-axis, positive y-axis, and in the upper area of the first quadrant) in addition to the two we started with (between the two charges on the x-axis). The values for the potential at each point is shown in the photo above.

The code for our custom program is as shown:

from visual import *

k = 8.988e9

#Charge 1

c1 = sphere(pos=(-2,0,0), radius=0.2,color=color.blue)

q1= -1e-9   #charge of Charge 1

#Charge 2

c2 = sphere(pos=(2,0,0), radius=0.2,color=color.red)

q2= 1e-9      #charge of charge 2

#C harge 3

c3 = sphere(pos=(0,-2,0), radius=0.2,color=color.blue)

q3= -1e-9   #charge of Charge 3

#Observation Locations

loc1= sphere(pos=(-1,0,0), radius = 0.1,color=color.green)

rc1= mag(loc1.pos-c1.pos)

rc2= mag(loc1.pos-c2.pos)

rc3= mag(loc1.pos-c3.pos)

Vc1= k*q1/rc1

Vc2=k*q2/rc2

Vc3=k*q3/rc3

Vnet= Vc1 + Vc2 + Vc3

L1 = label(pos=loc1.pos,xoffset=20,yoffset=20,text= "V=%1.2f" % Vnet)

loc2= sphere(pos=(1,0,0), radius = 0.1,color=color.green)

rc1= mag(loc2.pos-c1.pos)

rc2= mag(loc2.pos-c2.pos)

rc3= mag(loc1.pos-c3.pos)

Vc1= k*q1/rc1

Vc2=k*q2/rc2

Vc3=k*q3/rc3

Vnet= Vc1 + Vc2 + Vc3

L2 = label(pos=loc2.pos,xoffset=20,yoffset=20,text= "V=%1.2f" % Vnet)

loc3= sphere(pos=(0,2,0), radius = 0.1,color=color.green)

rc1= mag(loc3.pos-c1.pos)

rc2= mag(loc3.pos-c2.pos)

rc3= mag(loc1.pos-c3.pos)

Vc1= k*q1/rc1

Vc2=k*q2/rc2

Vc3=k*q3/rc3

Vnet= Vc1 + Vc2 + Vc3

L3 = label(pos=loc3.pos,xoffset=20,yoffset=20,text= "V=%1.2f" % Vnet)

loc4= sphere(pos=(3,0,0), radius = 0.1,color=color.green)

rc1= mag(loc4.pos-c1.pos)

rc2= mag(loc4.pos-c2.pos)

rc3= mag(loc1.pos-c3.pos)

Vc1= k*q1/rc1

Vc2=k*q2/rc2

Vc3=k*q3/rc3

Vnet= Vc1 + Vc2 + Vc3

L4 = label(pos=loc4.pos,xoffset=20,yoffset=20,text= "V=%1.2f" % Vnet)

loc5= sphere(pos=(1,3,7), radius = 0.1,color=color.green)

rc1= mag(loc5.pos-c1.pos)

rc2= mag(loc5.pos-c2.pos)

rc3= mag(loc1.pos-c3.pos)

Vc1= k*q1/rc1

Vc2=k*q2/rc2

Vc3=k*q3/rc3

Vnet= Vc1 + Vc2 + Vc3

L5 = label(pos=loc5.pos,xoffset=20,yoffset=20,text= "V=%1.2f" % Vnet)

Difference Between Cheating and Collaborating

An example of collaborating is when a group of students gather to come up with certain parts of a paper or lab report. They all pull their information together to calculate various forms of data, such as uncertainty and whatever calculations the experiment is asking for. Then, they go to their separate homes to formulate conclusions and finish the rest of the report that they will individually submit to their teacher.

Cheating, on the other hand, would be if the students never went home to complete their reports individually, and instead created one single report with the exact same wording. If they all turned in this one report, that would be cheating, because all their work is identical and no one went home to put in individual effort into one full, final report. 

Summary

In summation, we looked at electric circuits and how to properly illustrate them, as well as how changes in power affect the inner workings of a circuit. We also examined work in both gravitational and electrical fields, and how to accurately calculate how much work is done. In addition, we developed equations for measuring the electric potential difference (think potential energy) in an electrical field. Using VPython we ran simulations depicting several points of potential difference in an electrical field with two to three charges. We also briefly discussed what collaborating and cheating is, since we have a group project coming up soon.