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The impedance of an RLC series circuit is 8 ohms at resonance when f = 60hz but the impedance changes to 10 ohms when the frequency is increased to f = 80hz. Calculate the values of Capacitance, C and Inductance, L of the circuit.

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closed as off-topic by Aaron Stevens, M. Enns, Alfred Centauri, Jon Custer, LonelyProf Jan 11 at 6:56

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  • $\begingroup$ Hello, welcome to Physics Stack Exchange. This site is truly awesome for physics Q&A and one of the reasons it's so awesome is that we insist on high quality questions. You noted that your post doesn't show effort on your part, and honestly that's kind of a showstopper here. If there's no specific question, the post will be closed. That's just how it is. The exam situation etc. is completely irrelevant, and frankly when asking for help online mentioning that your're under time pressure is very likely to make others not want to help. We're all here on our own time, after all. $\endgroup$ – DanielSank Jan 11 at 0:55
  • $\begingroup$ I've removed the irrelevant parts of the post. I would really encourage you to work on the problem yourself and then ask for help here. Even if you get stuck on a basic conceptual issue, that's fine! You can ask for help on anything ranging from the meaning of terms to doing the calculations. $\endgroup$ – DanielSank Jan 11 at 0:56
  • $\begingroup$ I understand you have made some fair points thanks $\endgroup$ – Cinna Jan 11 at 1:03
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This won't be a full solution, but should get you started. Refer http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html for the basic equations:

At resonance, you have w0 = 1/sqrt(LC). We know w0 is 60, so you have one equation with 2 variables.

At resonance, the circuit impedance of a series RLC circuit is just R so you now know that.

In general, the impedance of a series RLC circuit is Z = sqrt(R^2 + (XL - XC)^2), where XL = 1/wL and XC = 1/wC. The second half tells you Z at 80Hz, so this falls out to another equation in L and C.

Solving the two equations in L and C for positive values (it's a safe assumption you don't have negative capacitance or impedance) gives a simple quadratic, which you should be able to solve in the normal manner.

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