Just one little question on the frequency band of the series RLC filter

[Lisa...]

Hey! I really need to find out how the width of the frequency band rejected depends on the resistance R of the following circuit:

http://img418.imageshack.us/img418/8168/rlc2wf.gif

I've done the following:
$$Q= \frac{\omega_0}{\Delta \omega}$$

so

$$\Delta \omega = \frac{\omega_0}{Q}$$

with

$$Q= \frac{\omega_0 L}{R}$$

Substitution gives:

$$\Delta \omega = \frac{\omega_0}{\frac{\omega_0 L}{R}}$$

$$=\frac{R}{L}$$


$$\Delta f= \frac{\Delta \omega}{2 \pi}$$

$$= \frac{\frac{R}{L}}{2 \pi}$$

$$= \frac{R}{2 \pi L}$$


Though my textbook says that

$$\Delta \omega = \frac{R}{2L}$$

... and it defines the delta omega as the frequency difference between the two points on the average power vs generator frequency curve where the power is half its maximum value...

So am I wrong or is the textbook's answer just confusing?

 

[Lisa...]

Anybody?! Please... it's due to tomorrow!

 

[kyle8921]

I would say that your calculations are correct and the textbook's answer may be confusing. In general, the width of the frequency band rejected in an RLC filter is dependent on the resistance R, as you have shown in your calculations. However, the exact formula for this relationship may vary depending on the specific circuit and the parameters being measured.

It is possible that your textbook is using a different definition for \Delta \omega, which is why the formula may look different. It is always important to clarify the definitions and assumptions being used when comparing different sources of information.

In addition, it is worth considering the limitations of the RLC filter and the assumptions made in its design. Real-world circuits may not behave exactly as predicted by theoretical models, and there may be other factors that affect the width of the frequency band rejected. As a scientist, it is important to continuously question and refine our understanding of physical phenomena.