An AM radio tuning circuit can be made by connecting an inductor, a resistor, an

Question

An AM radio tuning circuit can be made by connecting an inductor, a resistor, and a variable capacitor to an antenna, as shown in the figure. The inductor and resistor have fixed values. The capacitor is changed by a tuning knob until the resonance frequency of the RLC circuit is the same as that of the frequency of the radio station that is to be received. a) The frequency of WBLA is 1440 kHz. If the value of the inductor in the circuit is 0.300 mH, and the value of resistor is 400 ohms, calculate the value of the capacitor needed to pick up this radio station. Variable capacitors are costly, while variable resistors are cheap. Thus, your co-worker suggests that you should make this tunable circuit instead using a fixed capacitor, a fixed inductor, variable resistor Will this work? ___ If so, using the value of the capacitor you found in part a), calculate the value of the resistor needed to tune the circuit to a frequency of 720 kHz ___ If not, explain why it will not work. c) A second co-worker suggests that you should make this tunable circuit instead using a fixed capacitor, a fixed resistor, and a variable inductor. Will this work? ___

Explanation / Answer

a)
Resonance frequency of a series LCR circuit is given by
f = 1/{2SQRT[LC]}       ...(1)
L = 0.3 x 10-3 H
f = 1440 Hz
Squaring (1)
f2 = 1/42LC
C = 1/42f2L
= 1/[4 x 2 x (1440)2 x (0.3 x 10-3)]
= 4.07 x 10-5 F

b)
This will not work since the resonance frequency is independent of resistor.
In equation (1), we can see that the resonance frequency depends only on inductor and capacitor.

c)
This will work since the value of the inductance depends on the resonance frequency.

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