OK, I think I am doing this question right, but I'm not exactly sure. The question is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

For an RLC circuit with a resistance of [tex]16k\ohm [/tex], a capacitance of [tex]8.0\mu F [/tex] and an inductance of [tex]38.0H[/tex] what frequency is needed to minimize the impedance?

Well impedance is give by:

[tex] Z = \sqrt{R^2 + (X_C - X_L)^2} [/tex]

Putting [tex] X_C [/tex] and [tex] X_L [/tex] in terms of [tex] L, C, \omega [/tex] we then have:

[tex] Z =\sqrt{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2} [/tex]

Minimum impedance is acheived at resonance, so [tex] Z = R [/tex]

Thus we have:

[tex] R =\sqrt{R^2 + \left(\omega L - \frac{1}{\omega C}\right)^2} [/tex]

Solving this for [tex] \omega [/tex] yields:

[tex] \omega = \frac{1}{\sqrt{LC}} [/tex]

And frequency is given by: [tex] f = \frac{\omega}{2\pi} [/tex]

So solving [tex] f [/tex] for [tex] \omega [/tex] and substituting into the equation above gives:

[tex] f 2\pi = \frac{1}{\sqrt{LC}} [/tex]

Now solving for [tex] f [/tex] yields:

[tex] f = \frac{1}{2\pi\sqrt{LC}} [/tex]

And finally plugging in [tex] L,\,C[/tex] from above gives:

[tex] f = \frac{1}{2\pi\sqrt{(38.0H)(8.0\mu F)}} = 9.12Hz = 0.009kHz[/tex]

So I'm pretty sure there are going to be a few questions like this on my test tomorrow, so I just want to make sure I'm doing this correctly. Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Minimize Impedance - (eletromagnetism)

**Physics Forums | Science Articles, Homework Help, Discussion**