Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201815 AprilEvening ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Evening Shift
Mode
Online
Subject
Physics
Chapter
Communication System

JEE Main 2018 · 15 April · Evening Shift · Online · Physics · Communication System

The carrier frequency of a transmitter is provided by a tank...

The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance 49μH49 \mu \mathrm{H} and a capactiance of 2.5nF2.5 \mathrm{nF}. It is modulated by an audio signal of 12kHz12 \mathrm{kHz}. The frequency range occupied by the side bands is:

Options

  1. A18kHz−30kHz18 \mathrm{kHz}-30 \mathrm{kHz}
  2. B63kHz−75kHz63 \mathrm{kHz}-75 \mathrm{kHz}
  3. C442kHz−466kHz442 \mathrm{kHz}-466 \mathrm{kHz}
  4. D13482kHz−13494kHz13482 \mathrm{kHz}-13494 \mathrm{kHz}

Correct answer

C. 442kHz−466kHz442 \mathrm{kHz}-466 \mathrm{kHz}

Step-by-step solution

Given: Inductance, L=49μH=49×10−6H,capacitanceL=49 \mu \mathrm{H}=49 \times 10^{-6} \mathrm{H} , capacitanceC=2.5 nF=\mathrm{nF}=2.5 \times 10^{-9} F\mathrm{ F} Using ω=1LC=149×10−6×2.510×10−9=17×5×10−8=1087×5 or, 1087×5=2π×f=2×227×f or, f=10722=10422kHz=454.54kHz\begin{aligned} &\text{ Using } \omega=\frac{1}{\sqrt{L C}} \\ &=\frac{1}{\sqrt{49 \times 10^{-6} \times \frac{2.5}{10} \times 10^{-9}}} \\ &=\frac{1}{7 \times 5 \times 10^{-8}}=\frac{10^8}{7 \times 5} \\ &\text{ or, } \frac{10^8}{7 \times 5}=2 \pi \times f=2 \times \frac{22}{7} \times f \\ &\text{ or, } f=\frac{10^7}{22}=\frac{10^4}{22} \mathrm{kHz}=454.54 \mathrm{kHz} \end{aligned}Thereforefrequencyrange454.54±12kHzi.e.,Therefore frequency range 454.54 \pm 12 \mathrm{kHz} i.e.,442 kHz−\mathrm{kHz}-466 kHz\mathrm{kHz}
Practice Communication System on Quantrex Academy →

More from Communication System

The height of transmitting antenna is 180m and the height of the receiving antenna is… JEE Main 2023To radiate EM signal of wavelength λ with high efficiency, the antennas should have a… JEE Main 2023Match List-I with List-II List-I (Layer of atmosphere) List-II (Approximate height over… JEE Main 2023The amplitude of 15 ( 1000 ) is modulated by 10 ( 4 ) signal. The amplitude modulated… JEE Main 2023In satellite communication, the uplink frequency band used is: JEE Main 2023A transmitting antenna is kept on the surface of the earth. The minimum height of… JEE Main 2023A massage signal of frequency 3kHz is used to modulate a carrier signal of frequency 1 .… JEE Main 2023A carrier wave of amplitude 15V is modulated by a sinusoidal base band signal of… JEE Main 2023 Full Communication System list All JEE Main PYQs