Question

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

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.