hutchphd said:
A function generator is just what you need. And the oscilloscope and some education as to what to do. So describe your experimental process. What ...How ...why?
Okay, so my project is to take Calculus I concepts and apply it to a real-world application (be it engineering, business, or any life experience that can include calculus). I have been researching and fascinated by wireless induction for quite some time, so I figured why not center the project around that.
The research question I came up with is: If two inductors have the same perimeter and the same number of turns (thus made up of the same length of wire) but different shapes, will the inductance be equal?
My hypothesis is that they will not be equal because the cross-area section is different between the two shapes.
My first hurdle was to determine how I can have two shapes equal in length and perimeter. My answer to this was to take a circular coil for one inductor. The other inductor will have concave angles (like the shape of a star) to shrink the circular coil while maintaining the same perimeter (length to travel around the shape).
My paper would describe the different shapes by calculating their different areas inside the shape (so the circle would be
π(r)^2 and the other shape will be the sum of the area of triangles and a polygon).
My second hurdle was to eliminate any possible measurement errors. Because wrapping a wire around something by hand could cause kinks or inconsistent shapes, I decided to make a mold with my 3D printer. I will use the free website TinkerCad to do this.
I just made this just now very quickly for explanation purposes and will look 100% better once finished. Basically, that shaded area on the blue will be exactly the diameter of the wire so once I coil wire in that space it will not be able to form kinks. Also, that black piece will be used to compress the wire so that there are no spaces between the turns of the copper wire. I am going to use my calipers to find the diameter of the wire.
From here I will connect a capacitor to the circuit to create this:
Once I have the circuit together, I well induce a voltage and see the LC tank on the oscilloscope which would look something like this picture I drew:
I will calculate the area under each cycle (hence introducing calculus concept: integrals) and sum them up for a total area. I will do this for both inductors.
I will then figure out which inductor has the greater total area and deem it more efficient because it resonates greater current before zeroing out.
I think I could just take the area under the first cycle and can conclude the same thing now that I think about it.
Originally, I wanted to build and test the inductor using wireless inductance. It would have looked something like this:
The circle and wire common in both conductors would have been my receiving inductor. I was going to measure the efficiency of the inductors by measuring the current they produce on the receiving inductor. The reason I chose not to do this, is because I do not know how to incorporate calculus into the experiment. Unless I create a curve of the shape's area to show how the current output varies area. Then I could use calculus to measure the change in current at a given shape area.
