Question

In a series RCL circuit the generator is set to a frequency that is not the resonant frequency.

This nonresonant frequency is such that the ratio of the inductive reactance to the capacitive reactance of the circuit is observed to be 6.72. The resonant frequency is 240 Hz.

What is the frequency of the generator?

Answer 1

Answer: 624 Hz

Explanation:

If the ratio of the inductive reactance to the capacitive reactance, is 6.72, this means that it must be satified the following expression:

ωL / 1/ωC = 6.72

ω2 LC = 6.72 (1)

Now, at resonance, the inductive reactance and the capacitive reactance are equal each other in magnitude, as follows:

ωo L = 1/ωoC → ωo2 = 1/LC

So, as we know the resonance frequency, we can replace LC in (1) as follows:

ω2 / ωo2 = 6.72

Converting the angular frequencies to frequencies, we have:

4π2 f2 / 4π2 fo2 = 6.72

Simplifying and solving for f, we have:

f = 240 Hz . √6.72 = 624 Hz

As the circuit is inductive, f must be larger than the resonance frequency.