1. Suppose that your analog (traditional, non-digital) boom box has a tuner that contains a series R-L-C circuit, and the manual tuner dial adjusts the variable capacitor C, allowing you to change the radio station frequency to which the circuit is "tuned." We drive the series R-L-C circuit with the AC voltage from the radio's antenna (perhaps "amplified" a bit, to make its amplitude larger). a. (3 pts.) If your radio tuner circuit presently has an inductance of 17.50 uH, a capacitance of 0.1561 pF, and a resistance of 2.000 , what is the frequency of the radio station to which it is currently "tuned"? (Namely, what is the naturalresonant frequency? Assume negligible damping from the resistor.) Express your final answer in megahertz. Show your work. You do NOT need to show your work for the following question. Be sure to include units and sig. figs.! b.(3 pts.) Later, suppose you tune your radio's series-R-L-C circuit to KTUH FM fo-9030000 MHz), which occurs when its components have the following values: L-17.50000 , C-0.1 7751 16 pF, and R-2.000 You then leave its components alone, set at those values. Calculate the total impedance Z of this R-L-C circuit when it receives an input voltage signal with a frequency of, (i)f= 90.30000 MHz Z = (iif 90.50000 MHz Z- (this is the frequency of the next-closest channel on a digital radio tuner) iiis-90.70000 MHz Z- (this is the next-closest frequency that the FCC would allow another broadcaster to use in the same city as the 90.3 MHz station)