Design a circuit w/1 Ohm impedance

[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.

Homework Equations

Z_eq=Z_R+Z_L+Z_C
Z_R=R
Z_L=jωL
Z_C=-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)

 

[gneill]

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.

Homework Equations

Z_eq=Z_R+Z_L+Z_C
Z_R=R
Z_L=jωL
Z_C=-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.

 

[gneill]

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

 

[hogrampage]

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

 

[gneill]

At resonance, X_L=X_C, 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).

 

[gneill]

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?

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

where Z_eq=1.

 

[gneill]

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.