Question

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?

[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radiowave.]

Answer 1

Lower tuning, $f_1=800\times {10}^{3}Hz$

Upper tuning, $f_2=1200\times {10}^{3}Hz$

$L=200\times {10}^{-6}H$

Capacitance of the variable capacitor for $f_1$ is,

$C_1=1/\left({\omega }_1^{2}L\right)$

where, ${\omega }_1=2\pi f_1$

so, $C_1=198.1pF$

similarly, $C_2=88.04pF$

$⟹C\in [88.04pF,198.1pF]$