The tuning circuit in an FM radio receiver is a series RLC circuit with a 0.200

Question

The tuning circuit in an FM radio receiver is a series RLC circuit with a 0.200 H inductor.

Part A

The receiver is tuned to a station at 103.3 MHz . What is the value of the capacitor in the tuning circuit?

Part B

FM radio stations are assigned frequencies every 0.2 MHz, but two nearby stations cannot use adjacent frequencies. What is the maximum resistance the tuning circuit can have if the peak current at a frequency of 103.7 MHz , the closest frequency that can be used by a nearby station, is to be no more than 0.160 % of the peak current at 103.3 MHz ? The radio is still tuned to 103.3 MHz , and you can assume the two stations have equal strength.

Explanation / Answer

Part A:

C = 1 / (²L) = 1 / (4 ² f² L) = 1 / (4*3.141^2*103.3^2*10^12*0.20*10^-6) = 93.71 x 10^-12 F = 93.71 pF

Part B:

Maximum resistance in the tuning circuit = 0.16 / 100 = 0.0016 Ohms.

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