For tuning, the natural frequency i.e., the frequency of L-C oscillations should be equal to frequency of radio waves received by the antenna in the form of same frequency current in the L-C circuit. For tuning at 800 kHz, required capacitance $f_1$ = $\frac{1}{2\pi\sqrt{LC_1}}$ , $C_1$ = $\frac{1}{4\pi^2 L f_1^2}$ = $\frac{1}{4\pi^2 (200\times 10^{-6}) (800\times 10^3)^2}$ = 197.8 pF For tuning of 1200 kHz, required capacitance $f_2$ = $\frac{1}{2\pi\sqrt{LC_2}}$ , $C_2$ = $\frac{1}{4\pi^2 L f_2^2}$ = $\frac{1}{4\pi^2 (200\times 10^{-6}) (1200\times 10^3)^2}$ = 87.9 pF So, the variable capacitor should have a frequency range between 87.9 pF to 197.8 pF.