Frequency where reactence is zero

[kdrobey]

Homework Statement

At what frequency (in Hz) are the reactances of a 58 mH inductor and a 84 µF capacitor equal?

Homework Equations

Xl=1/2(Pi)fL
Xc=2(Pi)fC



3. The Attempt at a Solution [/b
F needs to be the same for both, so i got f by itself in both equations, then had them equal each other, giving me Xl2(Pi)L=1/2(Pi)XcC, but I am stuck from there

 

[Hootenanny]

Homework Statement

At what frequency (in Hz) are the reactances of a 58 mH inductor and a 84 µF capacitor equal?

Homework Equations

Xl=1/2(Pi)fL
Xc=2(Pi)fC
3. The Attempt at a Solution [/b
F needs to be the same for both, so i got f by itself in both equations, then had them equal each other, giving me Xl2(Pi)L=1/2(Pi)XcC, but I am stuck from there

I think you have misunderstood the question. The question wants to know for what frequencies are the reactances the same. In other words, find f such that X_c = X_l.

 

[kdrobey]

so if Xl=Xc, then 1/2(Pi)fl=2(Pi)fC? i tried that then got 1=(2pi fL)*(2pi fC). is that on the right track?

 

[nicksauce]

Yes, now just solve for f.

On a related note, wikipedia tells me
Xc = 1 / (2pi*f*C)
Xl = 2*pi*f*L
Which seems to be the opposite of what you have written, although it should still give the same answer.

 

[Hootenanny]

so if Xl=Xc, then 1/2(Pi)fl=2(Pi)fC? i tried that then got 1=(2pi fL)*(2pi fC). is that on the right track?

Looks good thus far .

 

[kdrobey]

got it! thanks a lot

 

[Hootenanny]

got it! thanks a lot

A pleasure .