Please answer all parts and be legible. Thank you!

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Please answer all parts and be legible. Thank you!

Please Answer All Parts And Be Legible Thank You 1 (137.82 KiB) Viewed 20 times

Tuning a Driven RLC Circuit O points possible (ungraded) Suppose you want a series RLC circuit to tune to your favorite FM radio station that broadcasts at a frequency of wo. Your antenna supplies an input voltage signal to the RLC series circuit. You cannot avoid having a resistance of R. The goal of this problem is find the values of the inductance L and the capacitance C. I(t)=1, cos(@t-o) R V(t)=V, cos(@t) L с HH (Part a) What is the amplitude of the current 10? Write your answer using some or all of the following: R, L, C, omega for wo and V_0 for V. Io = (Part b) If you want the amplitude of the current to be the maximum possible value, what condition must the inductance and capacitance satisfy? What is the maximum possible amplitude 1o,max if that condition is satisfied? There is no answer checking for the first half of this question. Write your answer for 10, max using some or all of the following: R, L, C, omega for wo and V_0 for V. 10,max
(Part c) You discover that your antenna is picking up a current signal of magnitude 11 from a second station that is broadcasting at a frequency wi which is very close to wo. The difference in the frequencies is characterized by (wo - wil/wi, where a > 0, but a < 1. a = = You would like your circuit to have a very small response to this second frequency. If you want 11 blo,max for b < 1, what values of L and C should you use? Assume that your antenna picks up the signal from each station with the same magnitude Vo. Use the fact that R2 /62 > RP to simplify some expressions. Note that the accepted algebraic answers will be the simplest approximation, I. e. the lowest order in a and b. You may also approximate wo + w1 2wo. Write your answer using some or all of the following: R, a, b, omega for wo and V_0 for Vo. L= C= (Part d) Let's try out some numbers. Suppose that R=0.112, wo = = (27) (89.7 MHz), and wi = (27) (89.5 MHz), and you would like b = 1/100. What are your values for capacitance and inductance? L= (in μH) C= (in pF)