Can the Impedance of Series RC and Parallel RL Circuits be Equal with Same R?

[phantomfx8192]

Homework Statement

Can a series RC circuit and a parallel RL circuit have the same impedance if the R is the same in both? What would the values of R, L and C have to be if they can? Why/why not, physically speaking?

Homework Equations

Zr=R
Z_c=1/iwC
Z_L=iwL

The Attempt at a Solution

I know in series the total impedance is the square root of each of the involved impedances squared, and if it's in parallel then it is the product of the two impedances divided by the square root of each of the involved impedances squared. So I have the two equations for impedance, but three unknowns and I'm not sure where to go next. Also, I have no intuition as to physically why or why not this statement would be true.

 

[rude man]

Homework Statement

Can a series RC circuit and a parallel RL circuit have the same impedance if the R is the same in both? What would the values of R, L and C have to be if they can? Why/why not, physically speaking?

Homework Equations

Zr=R
Z_c=1/iwC
Z_L=iwL

The Attempt at a Solution

I know in series the total impedance is the square root of each of the involved impedances squared, and if it's in parallel then it is the product of the two impedances divided by the square root of each of the involved impedances squared. So I have the two equations for impedance, but three unknowns and I'm not sure where to go next. Also, I have no intuition as to physically why or why not this statement would be true.

Z of series R-C is R - j/wC.
Y of parallel R-L is G - j/wL and Z =1/Y.

Equate the real and the imaginary components of the two Z's and see if there is a solution for L vs. C for any frequency w.