Purpose: We continue to look at basic circuits involving light bulbs. When, then, go into the general ideas of potential. We will see how potential energy, which is measured in joules, is related to the electric potential, which is measured in joules per coulomb.
How Bright Are These Bulbs?
We begin by developing a way to get two sets of light bulbs to be the brightest they can be by using two batteries and three wires. We found that running the batteries in series while running the bulbs in parallel is the most efficient way to distribute an equal amount of power to the bulbs and make it bright at the same time. The trick with using only three wires was that we had to come up with a way to make the bulbs parallel in a circuit. We did this by connecting two wires from the power supply to each bulb and have the metal next to the bulbs without wires connected touch. We, then, connect a single wire to the touching metal and connect it to the other end of the battery, closing the circuit.
The second experiment had us create a circuit that would make the light bulbs dim as possible. We found the connecting the batteries in parallel and the bulbs in series worked best.
Terminology
The white board shows what our circuit looks like drawn, without the proper format on the top left corner. On the top right corner, we are introduced to some symbols that represent some of the common things we will use in circuits. The bottom is the proper way to draw the two circuits we drew in the top left corner.
Heating A Cup Of Water
We take a look at how temperature changes as we heat water. The heating is caused by the power supply of some constant amount of volts. The next question we are given is: what happens the the change in temperature if we double the voltage?
Our group initially predicted that the slope for the change in temperature would just double. As it is seen on the graph produced on Logger Pro, the slope increased by more than double.
Why Is the Slope More Than Double?
We find that if we look at the relationship between voltage and current. We see that if we double the voltage, we double the current as well. Next, we know that the change in temperature is the same as saying heat going into the system per second, which we can say is power since power is joules per second. We, then, look at the relationship between power, voltage, and current. Since current doubles when voltage doubles, the doubles multiply together equating to four. Therefore, doubling the voltage gives us four times the power.
Reviewing Work
We go over a traditional problem involving work found in mechanics. We are to determine the amount of work done going up a slope. We found that there is no work done in the horizontal component but there is work done in the vertical component. This means that the work is independent of path.
Work Done Using E-Fields
We apply what we know about work to problems a little more relevant to our class. We compare the work done by three different paths. One path goes in the direction of the E-Field, another path goes at an angle, and the third path goes perpendicular to the E-Field. Every path, also, has the same length. We determined that the path parallel to the E-Field does the most work while the path perpendicular does no work at all. The reason the path A does the most work is because the E-Field produces a force in the same direction as the E-Field and because the path parallel to the force, it produces the most work. The other paths need projections of the path in the direction of the force or cannot be projected.
Deriving Electric Potential From Potential Energy
In finding the potential energy a charge contains in reference to another charge, we used the idea of the integral of force dotted with dr (or some distance). We know that potential is measured in joules per coulomb. So, we can say that we can integrate the electric field dotted with dr. This gives us a fundamental equation for electric potential. This is consistent, as potential energy is very similar to the electric potential, except potential energy has the second charge multiplied.
Potential Of Two Point Charges
Before we began the VPython activity, we had to make sure we understood how to get the potential of charges at some point with a test charge. We started with something simple on the same axis. We found the potential using superposition.
Finding Potentials At different Points
Using VPython, we were able to create three spheres with some charge. We placed these spheres in an x-y plane and created a formula that allowed us to put a test charge and some random location and find the potential due to all the charges in the vicinity. Finding the potential was just a matter of applying the superposition principle to potential of n amount of charges.
Potential Between A Positive And Negative Charge
If we are to determine the potential between two opposite charges, we find that the potential is zero in the central position between the two charges. This potential is zero across and infinite plane at the center. The potential is not zero outside this plane.
The difference between collaboration and plagiarism is displayed on the white board. Having someone do the work and copying it afterward is considered plagiarism while working in a group to get a solution and then, later, doing it without help (one's own interpretation) is collaborative.
Conclusion: We began by discussing the appropriate ways to label circuits and these appropriate ways make things neater to better interpret how the circuit behaves. We discussed the best ways to brighten and dim two light bulbs using the minimum amount of tools. We, then began to see the relationship between power and voltage. We found that power increases four times when voltage is doubled. We, also, revisited the definition of work and established that work is path independent. We, then, applied the concept in our derivation of electric potential, where we integrated the electric field dotted with dr. We found that potential follows the laws of superposition. This make calculations easier. We ended the day with a VPython activity, where we created a program that would allow us to calculate the potential at any position using a test charge.
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