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?

The range of frequency, [latex]  f_{1} is 800 * 10^{3} Hz [/latex].

The tuning frequency, [latex]  f_{2} is 1200 kHz = 1200 * 10^{3} Hz [/latex].

The inductance of LC circuit is [latex]  200\mu H = 200 * 10^{-6}H [/latex].

The resonant frequency is given by:

[latex]  f = \frac{1}{2\Pi \sqrt{LC}} [/latex].


[latex] f^{2} = \frac{1}{4 \Pi^{2} LC} [/latex].

[latex] \Rightarrow C = \frac{1}{4\Pi ^{2} Lf^{2}} [/latex].

[latex] \Rightarrow C_{1} = \frac{1}{4\Pi ^{2} Lf^{2}} [/latex].

[latex] \Rightarrow \frac{49}{4(22)^{2} * 200 * 10^{-6} (800 * 10^{3})^{2}} [/latex].

[latex] \Rightarrow C_{1} = 197.73pF [/latex].

[latex] \Rightarrow C_{2} = \frac{1}{4\Pi ^{2} Lf^{2}_{2}} [/latex].

[latex] \Rightarrow \frac{49}{4(22)^{2} * 200 * 10^{-6} (1200 * 10^{3})^{2}} F [/latex].

[latex] \Rightarrow C_{2} = 87.88pF [/latex].

Therefore, the range of the variable capacitor should be from 87.88pF to 197.73pF.

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