Question

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

• A. $18kHz-30kHz$
• B. $63kHz-75kHz$
• C. $442kHz-466kHz$
• D. $13482kHz-13494kHz$

Answer 1

Answer: (C)

$442kHz-466kHz$

$w=\frac{1}{\sqrt{LC}}$

$=\frac{1}{\sqrt{49\times {10}^{-6}\times \frac{2.5}{10}\times {10}^{-9}}}$

$=\frac{1}{7\times 5\times {10}^{-8}}=\frac{{10}^8}{7\times 5}=w$

$=\frac{{10}^8}{7\times 5}=2\pi \times f=2\times \frac{22}{7}\times f$

$\frac{{10}^8}{22\times 10}=f$

$\frac{{10}^7}{22}=f$

$\frac{{10}^4}{22}kHz=f$

$f=454.54kHz$

for frequency range

$454.54\pm 12kHz$

$442kHz-466kHz$