Find Resonant Frequency of L-R-C Series Circuit

AI Thread Summary
To find the resonant frequency of an L-R-C series circuit with a 1x10^-6 F capacitor, a 7.00 mH inductor, and a 90-ohm resistor, the correct approach involves using the relationship between inductive and capacitive reactance. The resonant frequency occurs when the reactance of the inductor equals that of the capacitor. The formula for resonant frequency is f = 1/(2π√(LC)), where L is the inductance and C is the capacitance. The initial confusion arose from incorrectly substituting the resistance value for capacitive reactance. Understanding the distinction between resistance and reactance is crucial for accurately calculating the resonant frequency.
jakeowens
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A L-R-C series circuit contains a 1x10^-6 F capacitor, a 7.00 mH coil and a 90 ohm resistor. What is its resonant frequency?


For this one I used the formula for capacitive reactance.

Xc=1/2pi*fC

After doing some algebra i isolated the frequency giving me :

f=(1/Xc)/2pi*C.

So i substitute all my values giving me:

f=(1/90)/2pi*1x10-6F...

The answer i get seems really wrong. Did I use the wrong formula?

Should i have used XL=2pi*fL?

I'm really at a loss for what to do with this problem

any help would be appreciated
 
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The resonance comes about because of the two energy-storing elements, the inductor and the capacitor. To figure out the resonant frequency, concentrate on the L and the C.

Hint, where are the reactance (complex impedance magnitude) of the inductor and capacitor equal?
 
right... and one more thing ... you seem to have substituted 90 for Xc ...
90 ohm is the resistance of the resistor given.. But Xc is the reactance of the capacitor ...

they are two different things
 

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