Need help with this exam question!

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Fred00

Joined Dec 10, 2006
2
Hi!

I'm having problem solving an old exam question, and would really like som help with it. The problem is about a parallel RLC circuit. I've done an expert drawing of the circuit in paint (okay, it's horrible, but at least you'll understand, I hope...).

The question is: Calculate the resonance frequency and Zin (at resonance).

I've calculated Zin = [ (1/(jwL+R1)) + 1/R2 + jwC ]^-1 (you may double check it to make sure it's correct)

But where do I go from there? How do I get rid of j to calculate Zin? How do I find the frequency?

/Fred
 

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Papabravo

Joined Feb 24, 2006
12,767
The usual method for getting a rational expression into real and imaginary parts is to make the demoninator real. The ususal way to do this is to multiply a complex number by its complex conjugate. If you multiply the denominator by the complex conjugate you must multiply the numerator as well that way everything remains unchanged.

This is by no means a straightforward or easy exercise. It takes extraordinary care to avoid making a fatal mistake. Well fatal for the result, not for your person.

Good Luck.
 

Dave

Joined Nov 17, 2003
6,970
Attached is the exercise I did to compute the Impedance of the circuit.

On edit ... corrected minor problem in a formula.
Great work JoeJester.

Am I right to question the fact that B2 = (1/0) in the penultimate equation and subsequently equates to B2 = 0 in the final equation?

Otherwise your mathematics seems flawless.

Dave
 

JoeJester

Joined Apr 26, 2005
4,130
Dave,

It was just reminding me that there was no reactance in branch 2, just as there was no resistance in branch 3 on the conductance side.

I should have just put a 0 in those spots ... but I guess I was having too much fun with the equation editor. :)

I edited the pdf to reflect the 0 in the G3 and B2 portion of the formula.
 

Dave

Joined Nov 17, 2003
6,970
Dave,

It was just reminding me that there was no reactance in branch 2, just as there was no resistance in branch 3 on the conductance side.

I should have just put a 0 in those spots ... but I guess I was having too much fun with the equation editor. :)

Edited to reflect the 0 in the G3 and B2 portion of the formula.
Hehe, no problem. The point is a fair one, if there is no resistive component in the branch then conductance has no meaning, whereas if there is no reactive component in the branch then susceptance has no meaning - in each case both equate to zero.

Its just the mathematical of us would see that the penultimate equation read as Z = 1/(c + 1/0) = 0 - picky as we are!

Edit in PDF noted.

Dave
 
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