12. A High-Pass Filter. One application of L-R-C series circuits is to high-pass or lowpass filters, which filter out either the low- or high-frequency components of a signal. A highness filter is shown in Figure, where the output voltage is taken across the L-R combination. (a) Derive an expression for (V_out / V_s), the ratio of the output and source voltage amplitudes, as a function of the angular frequency ω of the source and R, L, and C parameters. (b) Show that when ω is small, this ratio is proportional to ω and thus is small, and (c) show that the ratio approaches unity in the limit of large frequency. [15分, find the reactance of L and C to construct the voltage and current]