(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In the AC circuit shown, the potential difference across the capacitor and the resistor, V(BD), is 24 V(rms). Similarly, the potential difference across the inductor and the resistor, V(AC) is 24 V(rms). What is the frequency of the source?

http://img52.imageshack.us/img52/8039/lolkve.png [Broken]

2. Relevant equations

V = sqrt(V(R)^2 + V(L)^2)

V = sqrt((I(rms)*R)^2 + (I(rms)*X(L))^2)

V = sqrt(V(R)^2 + V(C)^2)

V = sqrt((I(rms)*R)^2 + (I(rms)*X(C))^2)

X(L) = 2pi*f*L

X(C) = 1/(2pi*f*C)

3. The attempt at a solution

So, immediately I saw that I could use the two voltage equations above to solve for either I(rms) or f, since both are constants. I decided to solve for f, as it is what the question is asking for. I arbitrarily took the inductance equation and rearranged for I(rms).

http://img201.imageshack.us/img201/7150/codecogseqn1s.gif [Broken]

http://img259.imageshack.us/img259/1027/codecogseqn2w.gif [Broken]

http://img138.imageshack.us/img138/8778/codecogseqn3.gif [Broken]

http://img3.imageshack.us/img3/3735/codecogseqn9.gif [Broken]

Plugging that into the other equation:

http://img705.imageshack.us/img705/7231/codecogseqn5x.gif [Broken]

Simplified into:

http://img252.imageshack.us/img252/7870/codecogseqn7.gif [Broken]

http://img849.imageshack.us/img849/9776/codecogseqn8.gif [Broken]

Essentially, I ended up with something like:

http://img710.imageshack.us/img710/2517/codecogseqn10.gif [Broken]

It's at this point that I basically gave up. I plugged the equation into wolframalpha, got around 89 Hz, and decided that that was a reasonable number.

Now, my question is, did I approach the problem incorrectly? Or is this the right way to do it, and the numbers are ACTUALLY this complicated? Or did I just make an algebraic error somewhere? Any help would be appreciated.

There are 3 more questions, but I need the frequency in order to solve them. Once I have it, the other 3 questions can be easily solved.

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# Homework Help: RLC circuit problem set

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