Physics Lab, Transient response of LCR circuit, lorentzian curve

[austeane]

I wasn't exactly paying much attention during our lab, partially because it was right in the middle of midterms and I wanted to solely focus on those. Now it is coming back to bite me as I am not entirely sure how to complete my lab report, or the theory behind the lab really.
If you would like to read the lab, it is here https://www.dropbox.com/s/mi34hd6yfmdisok/Experiment3.pdf

I started to write a couple of paragraphs describing what I did, and the data I took, but it would basically be summarizing the lab, and that is written concisely in the link above.

If anyone is worried about opening links, I can re-write or copy-paste the above here, just let me know.



I am hoping to gain a better understanding of what is going on.

I understand that if you have a current going through a LC circuit (negligiable resistance), the energy bounces back and forth between the capacitor and the inductor. It takes energy to get the inductor moving since it resists a change in current, that can come from an imbalance of charge on the capacitor. Once the current is going, the inductor wants to sustain it and pushes it through to create an imbalance the other way on the capacitor. It goes back and forth indefinitely (assuming zero resistance).
The resistor "dampens" it, in that it pushes less each time going from L to C and back again, with the resistor converting the energy to heat.

Time could have certainly atrophied my understanding of circuits, so any clarification/correction on the above would be appreciated.

When we had a wave-generator pushing our square wave through, wouldn't that serve to sustain the wave? Thinking about it more, it must have been AC and thus it was just a new current each time... But wouldn't the old currents take a while to die out and then interfere with the new ones?



I bet once I get a better understanding of a couple of these things, the rest will fall in place.

I would appreciate an explanation of where the first formula (Vr/Vo) in the lab comes from, and how to express it in terms of the other things (γ,ω).

We were able to do the first part without issue.

For part two, I wouldn't mind knowing what a Lorentzian curve is, and how it compares to say a Gaussian.

The last part of the lab, determining the relationship between the transient and AC responces, I am not sure on... Once I have the AC response done, I should be able to figure it out but I wouldn't mind some guidance.

Aslo, what would a third parameter be and why would it be needed.

Thanks!
Austin Wallace

 

[anathema]

Hello Austin,

First of all, I completely understand the struggles of balancing midterms and lab work. It can be overwhelming at times, but I'm glad you are reaching out for help.

From what you have described, it seems like you have a good understanding of the theory behind the lab. Just to clarify, an LC circuit is a type of electrical circuit that consists of an inductor (L) and a capacitor (C) connected together. When a voltage is applied to the circuit, the energy oscillates back and forth between the inductor and the capacitor, creating a continuous flow of energy.

The resistor in the circuit serves to dampen this oscillation by converting the energy into heat. This is known as damping. Without the resistor, the oscillation would continue indefinitely, but with the resistor, it eventually dies out.

Now, the first formula (Vr/Vo) in the lab is known as the voltage ratio. It is the ratio of the voltage across the resistor (Vr) to the voltage across the whole circuit (Vo). This formula is derived from the theory of the LC circuit and can be expressed in terms of other variables such as γ and ω. γ represents the damping coefficient, which determines how quickly the oscillation dies out. ω is the angular frequency of the oscillation.

Moving on to part two, a Lorentzian curve is a type of curve that is often used to describe the shape of certain physical phenomena, such as atomic spectra or particle interactions. It is similar to a Gaussian curve, but with a slightly different shape. In this lab, the Lorentzian curve is used to describe the shape of the voltage response of the LC circuit.

As for the last part of the lab, determining the relationship between the transient and AC responses, it involves analyzing the behavior of the circuit when a voltage is suddenly applied to it (transient response) and when a continuous alternating voltage is applied (AC response). A third parameter may be needed to fully describe the behavior of the circuit, depending on the specific conditions and variables involved.

I hope this helps to clarify some of the concepts and equations in the lab. If you have any further questions or need more guidance, don't hesitate to reach out. Good luck with your lab report!