LRC Series Circuit Voltage amplitude question.

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Homework Help Overview

The discussion revolves around a problem related to LRC series circuits, specifically focusing on the angular frequencies at which the voltage amplitudes across the resistor and inductor reach their maximum values.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to determine the angular frequencies by solving an equation and optimizing functions related to voltage amplitudes. They express uncertainty about the process and seek assurance on their approach.
  • Another participant suggests using impedance values and voltage divider equations, prompting a consideration of how component impedance varies with frequency.
  • Further, a participant questions the definition of the "LRC circuit," indicating a need for clarity on the problem context.

Discussion Status

The discussion includes various attempts to derive expressions for voltage amplitudes and their optimization. Some participants have provided insights into the mathematical approach, while others are exploring definitions and clarifications. There is an acknowledgment of the complexity involved in deriving the necessary functions.

Contextual Notes

Participants mention the challenge of deriving functions and the complexity of the derivatives involved, indicating that the problem may have multiple steps and interpretations. The original poster notes the problem's classification as Level III, suggesting a higher difficulty level.

BrettJimison
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Homework Statement


Hello All,

I have a question:
In a LRC Series circuit:

At what angular frequency is the voltage amplitude across the resistor at a maximum value?
At what angular frequency is the voltage amplitude across the inductor at a maximum value?

Homework Equations



\omega = \sqrt{(\frac{1}{LC})-(\frac{R^{2}}{4L^{2}})}

The Attempt at a Solution


[/B]
Im just looking for some assurance.

Do I simply just solve the equation for R ( for the first question) and optimize the function?

(And then just Solve the eqn for L for the second question and do the same?)

Seems to simple and my book has this as a Level III problem.
 
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Actually I left one part out:

How do I find voltage amplitude? I know I will optimize a function somewhere but I'm not sure which one...
 
If you work with impedance values (complex form of "resistance") for the components, then you can write the expressions for the various voltages as voltage divider equations. You might also ponder how the impedance of the various components vary with frequency.
 
BrettJimison said:

Homework Statement


Hello All,

I have a question:
In a LRC Series circuit:
Define your "LRC circuit".
 
I got it, thanks though!

I would explain how but it requires A LOT of steps. The derivative for d(Vl)/d(omega) is really nasty.

for a I got: \omega =\frac{1}{\sqrt{LC}}

for b I got: \omega = \frac{1}{\sqrt{LC-\frac{(RC)^{2}}{2}}}

Part a was easy, part b required me to take the derivative of V L (voltage amplitude across inductor) with respect to omega.

The function I derived was: V_{L}= \frac{VL\omega}{\sqrt{R^{2}+(\omega L-\frac{1}{\omega C})^{2}}}

too much latex to show, but in the end ,

\frac{dV_{L}}{d\omega }=0 when \omega = \frac{1}{\sqrt{LC-\frac{(RC)^{2}}{2}}} in the end.

...In case anyone was interested..
 

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