What is the value of the inductor in this capacitor and inductor problem?

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Homework Help Overview

The problem involves a capacitor charged by a battery and subsequently connected to an inductor, with the goal of determining the value of the inductor based on the angular frequency of oscillation. The subject area pertains to oscillations in electrical circuits, specifically involving capacitors and inductors.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between angular frequency, inductance, and capacitance, questioning the correct interpretation of the variables involved. There is confusion regarding the use of charge versus capacitance in the relevant formula.

Discussion Status

Some participants have provided guidance on the correct interpretation of the variables in the formula, while others have noted potential misunderstandings regarding the problem's parameters. There is an acknowledgment of differing interpretations of the capacitor's charge and its implications for capacitance.

Contextual Notes

The problem does not specify whether the capacitor is fully charged to the battery voltage, leading to uncertainty about the minimum capacitance value. This ambiguity may affect the calculation of the inductor's value.

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Homework Statement


A capacitor is charged with a 12 volt battery until there is 3 μc of charge on the capacitor. The capacitor is then connected to an inductor. The angular frequency of the resulting oscillation is 1.25 x 105 rad/s. What is the value of the inductor?

Homework Equations


LC: ω = 1/sqrt(LC)

The Attempt at a Solution


rearranging the equation gives: L=1/(ω2C)=1/(1.25E5rad/sec)(3E-6C)

This gave me an answer of 2.67 H, which is incorrect. Am I not using the correct equation for this type of problem?
 
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What do you think C is in the formula for the angular frequency ω = 1/sqrt(LC)??
 
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Hi! Your answer is going to be wrong for two reasons, I think. You've forgotten there's a squared term? The C in the formula is capacitance, not charge.

I'm curious, though --- does your textbook give you its correct answer??
 
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Sorry I know C is for capacitance I don't know why I did that, I still can't figure this out though. What term is supposed to be squared in this equation? It does give me the correct answer, it is supposed to be 256 μH.
 
Nevermind I figured it out thanks guys.
 
Chase11 said:
the correct answer, it is supposed to be 256 μH.
The problem says the capacitor is given a charge of 3 μC from the battery; though it doesn't state that the capacitor is fully charged to 12V. This tells us that the capacitance is at least a certain minimum value---it could be larger and just not charged right up to 12V. We aren't told exactly.

So IMHO the correct answer is that L ≤ 256μH

This would make a good trick question, allocating 1 mark for 256 uH and 1 mark for the inequality.
 
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