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A radio can tune over the frequency range of a portion of MW broadcast band (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of `200 mu H`, what must be the range of its variable capacitor ? |
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Answer» The range of frequency (v) of a radio is 800KHz to 1200 KHz. Lower tuning frequency, `v_(1)=800KHz=800xx10^(3)Hz` Upeer tuning frequency, `v_(2)=1200KHz=1200xx10^(3)Hz` Effective inductance of circuitL=200`muH=200xx10^(-6)H` Capacitance of variable capacitor for `v_(1)` is given as, `=(1)/(omega_(1)^(2)L)` Where, `omega_(1)=` Angular frequency for capacitor `C_(1)` `=2piv_(1)=2pixx800xx10^(-3) "rad"s^(-1)` `therefore C_(1)=(1)/((2pixx800xx10^(3))^(2)xx200xx10^(-6))` `=1.9809xx10^(-16)F=198.1pF` Capacitanc e of variable capacitor for `v_(2)`. ` =(1)/(omega_(2)^(2)L)` Whre, `omega_(2)=` angular frequency for capacitor `C_(2)` `=2piv_(2)=2pixx1200xx10^(3)"rad"s^(-1)` `thereforeC_(2)=(1)/((2pixx1200xx10^(3))^(2)xx200xx10^(-6))` =`88.04 pF` Hence, the range of the variable capacitor is from 88.04pF to 198.1 pF. |
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