How Do You Calculate R and C for a Series Impedance of 500∠-36.1° at 10kHz?

[zealeth]

Homework Statement

Compute values for R and C such that the total series impedance Z=500\angle(-36.1^o) when f=10kHz.

Homework Equations

ω=2\pif
KVL
Z_C = -j*(1/(ωC)) = 1/(jωC) where j=\sqrt{-1}

The Attempt at a Solution

Seems like a pretty straightforward problem, I seem to be missing an equation somewhere but not sure what else I could use here.

ω=2*\pi*10*10³ = 62832 rad/s
Z_eq=500\angle(-36.1^o) = R - j/(ωC) = R - j/(62832*C)

And here I am left with 1 equation and 2 variables, any ideas on what else I could use to solve this problem?

 

[gneill]

Homework Statement

Compute values for R and C such that the total series impedance Z=500\angle(-36.1^o) when f=10kHz.

Homework Equations

ω=2\pif
KVL
Z_C = -j*(1/(ωC)) = 1/(jωC) where j=\sqrt{-1}

The Attempt at a Solution

Seems like a pretty straightforward problem, I seem to be missing an equation somewhere but not sure what else I could use here.

ω=2*\pi*10*10³ = 62832 rad/s
Z_eq=500\angle(-36.1^o) = R - j/(ωC) = R - j/(62832*C)

And here I am left with 1 equation and 2 variables, any ideas on what else I could use to solve this problem?

Actually you're left with two equations, each in one variable. Note that the impedance has two terms, one real and one imaginary. The real and imaginary components are separate. For example, the real part of the impedance (the resistance) is independent of frequency.