Design a circuit w/1 Ohm impedance

• Engineering
hogrampage

Homework Statement

Design a suitable combination of resistors, capacitors, and/or inductors which has an equivalent impedance at ω=100 rad/s of 1Ω using at least one inductor.

Zeq=ZR+ZL+ZC
ZR=R
ZL=jωL
ZC=-j/ωC

The Attempt at a Solution

I really am not sure how to start. I can see this being a fairly simple problem, but I just can't seem to wrap my head around it. I have read through the chapter numerous times, and I don't see anything else that could help at all.

scootypuffsnr
maybe
1= R + jwL +j/wC

1= R + j(wL+1/wC)

1= R + j(100L+1/100C)

easy one can be R =1, L=.01, C= -0.01
which equals 1 = 1+ j(0)

Mentor

Homework Statement

Design a suitable combination of resistors, capacitors, and/or inductors which has an equivalent impedance at ω=100 rad/s of 1Ω using at least one inductor.

Zeq=ZR+ZL+ZC
ZR=R
ZL=jωL
ZC=-j/ωC

The Attempt at a Solution

I really am not sure how to start. I can see this being a fairly simple problem, but I just can't seem to wrap my head around it. I have read through the chapter numerous times, and I don't see anything else that could help at all.

What do you know about LC or RLC circuits? Any special properties come to mind?

hogrampage
ω0=$\frac{1}{\sqrt{LC}}$

and

$\alpha$=$\frac{1}{2RC}$

Underdamped when $\alpha$<ω0, which has imaginary components.

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Mentor
What conditions exist when a series RLC circuit are at resonance (ω = ωo)?

hogrampage
At resonance, XL=XC, but that would just make them cancel out so I'm not sure what to do.

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Mentor
At resonance, XL=XC, but that would just make them cancel out so I'm not sure what to do.

Well, if they cancel out, what remains?...

hogrampage
R, but I'm supposed to use at least one inductor. I must be over-analyzing this (I think about these things too much lol).

Mentor
R, but I'm supposed to use at least one inductor. I must be over-analyzing this (I think about these things too much lol).

Hmm, doesn't the "L" in "LC" count as an inductor?

hogrampage
Yes, but I'm lost as to how to find the value(s). It isn't making sense to me. I don't even know which equation(s) to use. I have looked at the equations in the book and examples, and they aren't helping at all. No matter what, they always know at least one of the impedance values.

EDIT: Am I going anywhere with the below equation?

Zeq=jω$\frac{1}{4\pi^{2}f^{2}C}$-$\frac{j}{ωC}$

where Zeq=1.

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Mentor
I'm not sure what's confusing you Choose any L and a corresponding C that cancels it for the given frequency of operation --- then bang in a 1 Ohm resistor and you're home free.