anonymous 4 years ago 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)

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$