Resonance in Electrical Circuit

[just.karl]

(a)Find the frequency at which a 33 uF capacitor has the same reactance as a 33 mH inductor. (b) What is the resonance frequency of an LC circuit made with this inductor and capacitor. Well I believe the equation I use is 1 / (2 Pie $$\sqrt{}LC$$) but when I use it I come out with a answer very different from the real answer. Am I going about the right way with this problem? Thanks!

 

[marcusl]

You are using

$$f=\frac{1}{2\pi \sqrt{LC}}$$

and this is the correct equation. Perhaps recheck your numbers?

 

[thomate1]

I can confirm that you are on the right track with your approach to the problem. The equation you mentioned, 1 / (2 Pie \sqrt{}LC), is the correct formula for calculating the resonance frequency of an LC circuit. However, it is important to note that the units of the inductance and capacitance must be consistent for the formula to work. In this case, the 33 uF capacitor and 33 mH inductor have different units (farads and henrys, respectively), which may be the reason for the discrepancy in your answer.

To ensure accurate results, it is important to convert all units to the same base unit before plugging them into the formula. In this case, we can convert the capacitance to its base unit of farads by multiplying it by 10^-6, and the inductance to its base unit of henrys by multiplying it by 10^-3. This results in a capacitance of 0.000033 F and an inductance of 0.033 H. Plugging these values into the formula yields a resonance frequency of approximately 5.77 kHz.

In conclusion, your approach to the problem is correct, but it is important to ensure that all units are consistent before using the formula for resonance frequency. I hope this helps clarify the issue.