Question

Radios take advantage of resonance in RLC circuit.  In a particular radio the tuning dial is attached to a variable capacitor in which by rotating the dial you change the separation distance between the plates. The antenna of the radio can pick up a wide range of AM and FM radio frequencies, but the RLC circuit within the radio can "tune-in" on one particular radio frequency. How can this particular radio "tune-in" on a specific radio station?

Answer 1

resonance occuered in RLC circuit only when capacitive reactance XC  = inductive reactance XL

Xc  =(1/(2fC))

XL = (2fL)

these reactaces are depends on the frequency of current flowing through it.when we tune by adjusting the seperation between capacitive plates the capacitive reactance( XL ) also changes and at a perticular distance both reactance would be equal (resonance occured). if resonance uccured there will be low impedence and high current would flow through the circuit at this perticular frequency that we tuned only.this resonace current sense by the help of electronic circuit.

mathematically Z =   

where XL = XC occured impedence become minimum and current become maximum

R2 + (XL - Xc)2)

channel 1 = frequency 1 = 1/2(LC₁)

channel 2= frequency2 = 1/2(LC2)

channel3 = frequency3 = 1/2(LC₃)

etc...