Q 12-14-197JEE MainJEE Main 2018 (15 Apr, Shift 2)Medium
The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance $49\ \mu\text{H}$ and a capacitance of $2.5\ \text{nF}$. It is modulated by an audio signal of $12\ \text{kHz}$. The frequency range occupied by the side bands is:
Answer: (C) $442\ \text{kHz} - 466\ \text{kHz}$
Carrier frequency:
$$f_c = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{49\times10^{-6}\times2.5\times10^{-9}}} = \frac{1}{2\pi\times3.5\times10^{-7}} \approx 455\ \text{kHz}$$
The side bands occupy $f_c \pm f_m$:
$$455 - 12 = 443\ \text{kHz} \quad\text{to}\quad 455 + 12 = 467\ \text{kHz}$$
which matches $442\ \text{kHz} - 466\ \text{kHz}$.
Solution by Sreeraj P, M.Sc Physics