Rlc filter consider the following rlc circuit: + − vs c + − vc i l + vl − r + − vr (a) write down the impedance of a series rlc circuit in the form zrlc(ω) = a(ω) + jx(ω), where x(ω) is a real valued function of ω. (b) write the transfer function from vs to vr — the voltage drop across the resistor. (c) for the different specific values for r, l,c given by different cases (underdampled, overdamped, and critically damped) in the previous hw, use a computer to sketch plots of the magnitude of the transfer function above. (d) to see how the values of r, l,c impact the impedance at different frequencies, run the included jupyter notebook rlcsliders. ipynb. the script will generate two plots, the transfer function of the circuit as a function of frequency and the location of the eigenvalues in the imaginary, real plane. explain what happens at the following sets of values, and why it is interesting: