Question 2 You\'ve decided to build a radio to listen to your favourite FM radio

Question

Question 2 You've decided to build a radio to listen to your favourite FM radio station, which broadcasts at 106.7 MHz. For the tuner, you'll be using an RLC circuit, but the only inductor you happen to have on hand has a value of 0.420 pH. If you only care about listening to your favourite station, what value of capacitor should you use in the tuning circuit? Unfortunately, there's another radio station -which you don't want to listen to- at a nearby frequency of 107.1 MHz. To prevent any interference from this 107.1 MHz radio station, you want the peak current from it to be no more than 0.190% of the peak current from your favourite 106.7 MHz station. What value of resistor should you use in your RLC circuit? (Assume the two stations have the same strength.)

Explanation / Answer

for resonance,

xL = xC

2 pi f L = 1 / (2 pi f C)

4 pi^2 f^2 L C = 1

4 x pi^2 x (106.7 x 10^6)^2 (0.420 x 10^-6) (C) = 1

C = 5.30 x 10^-12 F or 5.30 pF .......Ans  

at f = 107.1 x 10^6 Hz

XL = 282.63 ohm

Xc = 1/(2 pi f C) = 280.52 ohm

(.190 /100) Z = R

526.326 R = sqrt[ R^2 + (282.63 - 280.52)]

(526.326 R)^2 = R^2 + 2.11

R = 2.76 x 10^-3 ohm .....Ans

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