QJEEM18Ph639d: JEE Main 2018 Physics - Class 12 JEEM18Ph639d Solution: The carrier frequency of a transmitter is provided by a tank…

Question

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The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance 49

μ

H and a capacitance of 2.5 nF. It is modulated by an audio signal of

12

k H z .

The frequency range occupied by the side bands is :

Accepted Answer

The tank circuit of an inductance and a capacitance is

JEE Main 2018 (Online) 15th April Evening Slot Physics - Communication Systems Question 93 English Explanation

We know that

$ω = \frac{1}{\sqrt{L C}} = \frac{1}{\sqrt{49 μ H \times 2.5 n F}} = \frac{1}{\sqrt{49 \times 10^{- 6} \times 2.5 \times 10^{- 9}}}$

$\Rightarrow ω = \frac{1}{\sqrt{49 \times 25 \times 10^{- 16}}} = \frac{1}{7 \times 5 \times 10^{- 8}}$

Since $ω = 2 π f$

$\Rightarrow f = \frac{ω}{2 π} = \frac{1}{7 \times 5 \times 10^{- 8} \times 2 π}$

$\Rightarrow f = 454.5$ kHz

Given carrier frequency is modulated by audio signal of 12 kHz. Therefore,

f = 454.5 kHz $\pm$ 12 kHz

$\Rightarrow$ f = 442 kHz $-$ 466 kHz

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