Question

2nd Order Elec Circuits: For a strictly parallel RLC circuit with parameters R, L=275mH, and C=10nF, find the value of R that will yield a damped frequency of 12 krad/s. (Illustration attached in the first comment)

Answer 1

Recall that the characteristic equation of a parallel RLC circuit is:
\[s ^{2}+2\alpha(s)+\omega ^{2} _{o}\] where \[\alpha = 1/2RC\]is known as the neper frequency: it reflects the effect of R and \[\omega _{o} = 1/LC\]In the problem, you're given \[\alpha = 12krads/s\]\[C = 10nF = 1x10^{-8}nF\]
With this information, you can solve for R.
\[12000rads/s = 1/(2(1x10^{-8})R)\]\[12000rads/s = 1/(2x10^{-8}R)\]\[12000rads/s = 50000000/R\]\[12000R = 50000000\]\[R = 4166.67 \Omega\]