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

[Chase11]

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?

 

[ehild]

What do you think C is in the formula for the angular frequency ω = 1/sqrt(LC)??

 

[NascentOxygen]

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??

 

[Chase11]

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.

 

[Chase11]

Nevermind I figured it out thanks guys.

 

[NascentOxygen]

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.