What is the inductance of the inductor in a series RCL circuitwith a resonant fr

Question

What is the inductance of the inductor in a series RCL circuitwith a resonant frequency of 640 Hz if the only other element inthe circuit is a 1.2-µF capacitor? I think the answer is 52 mH acc to my classmate but I have noidea how he comes up with it. What is the inductance of the inductor in a series RCL circuitwith a resonant frequency of 640 Hz if the only other element inthe circuit is a 1.2-µF capacitor? I think the answer is 52 mH acc to my classmate but I have noidea how he comes up with it.

Explanation / Answer

We know that the resonant frequency is given by                       fo =1/2LC                           Then for the inductor we get                       L = 1/42fo2C                           =1/4(3.14)2(640Hz)2(1.2*10-6F)                          = 1/19.384762368                          = 0.05158H                          = 51.58mH                           ˜52mH                          = 51.58mH                           ˜52mH                                                

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