b. (3 pts.) Later, suppose you tune your radio\'s series-R-L-C circuit to KTUH F
ID: 1377061 • Letter: B
Question
b. (3 pts.) Later, suppose you tune your radio's series-R-L-C circuit to KTUH FM J90.30000 MHz), which occurs when its components have the following values: L 17.50000 puH, C 30.1775116 pF, and R 1.0002. 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 390.30000 MHz Z (ii) 90.50000 MHz this is the frequency of the next closest channel on a digital radio tuner (iii 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) Carry 7 significant figures in your calculation, even though your final answers for Z may have fewer than 7 Beware of round-off errors! [Note: Since your circuit is already "tuned" to 90.3 MHz, 90.3 MHz is its natural (resonant) frequenc so y, the L & C should together contribute zero impedance for incoming signals at exactly 90.3 MHz. Only R contributes any impedance in this case. However, for incoming signals whose frequencies are not at the resonant frequency, like 90.5 or 90.7 MHz, the impedance of a circuit tuned to 90.3 MHz is much greater! This impedance grows dramatically as the incoming frequency gets farther from the resonant frequency. Thus, the L-C part of the circuit is able to kill off incoming signals at all other unwanted frequencies (such as radio signals at other nearby frequencies) using high impedance, and the only signal that survives (with lowest impedance is the one at the circuit's "tuned" (resonant) frequency.]Explanation / Answer
In R-L-C series circuit impedence Z is given by:
Z = ( R2 + ( XL - Xc )2 ) 1/2
( a ) In this case , since circuit is at natural resonance frequency. so XL = Xc
So Z = R = 1.000000 ohm
(B) XL = w L = 2*pie*f*L = 9.94 ohm
Xc = 1/ wc = 1/ 2*pie*f*c = 9.91*106 ohm
so Z = 9911829 ohm
(C) XL = 9.96 ohm by formula used above
Xc = 9.89*106 ohm
Z = 9889990 ohm
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