A radio tuner is built by connecting an L=0.41mH inductor and variable capacitor

Question

A radio tuner is built by connecting an L=0.41mH inductor and variable capacitor in series with an antenna. The driving voltage is provided by the radiowaves that pass through the antenna, and the total internal resistance of the circuit is R=1.2Ohms.


(a) To what capacitance should the variable capacitor be adjusted to tune the radio to 520kHz?

(b) What is the quality factor of the circuit with the capacitance you found in (a)?

(c) If another station operates at 470kHz with the same amplitude at your location, what is the ratio of the output voltage due to this background signal to the output of the signal for which the circuit has been tuned? The output voltage is the voltage across the capacitor. (See Example 32.8)

(d) Find this same ratio if the other station operates with the same amplitude at frequency 515kHz

Explanation / Answer

a.)w=1/sqrt(LC)

C=1/w^2L

C=1/(2*pi*700000)^2((0.48x10^-3)=1.08 x 10^-10 F

b.)Q=wL/R=(2*pi*700000)(0.48 x 10^-3)/2.8=754

c.)V=E(1/wC)/sqrt((wL-1/wC)^2+R^2)

V2=E(7.23)

V1=E(751.8)

V2/V1=0.00963

d.)Do the same as above and you will get ratio=0.0928

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