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Question: In the given detector circuit, the suitable value of carrier frequency is :- ![](https://www.vedan...

In the given detector circuit, the suitable value of carrier frequency is :-

(A) 109Hz \ll {10^9}Hz
(B) 105Hz \ll {10^5}Hz
(C) 109Hz \gg {10^9}Hz
(D) None of these.

Explanation

Solution

In this detector circuit, using the values for the resistance and the capacitance, we can find their product. Now using the condition for the carrier frequency in detector circuit that is, 1fcRC\dfrac{1}{{{f_c}}} \ll RC, we can find the suitable value of the carrier frequency.

Formula Used In this solution we will be using the following formula,
1fcRC\dfrac{1}{{{f_c}}} \ll RC
where fc{f_c} is the carrier frequency,
RR is the resistance and
CC is the capacitance

Complete Step by Step Solution
For a detector circuit, the carrier frequency, the resistance and the capacitance are all related by the formula,
1fcRC\dfrac{1}{{{f_c}}} \ll RC
Now we can take reciprocal on both the sides. So we will get,
fc1RC{f_c} \gg \dfrac{1}{{RC}}
The inequality sign also gets reversed on taking the reciprocal.
Now we are given in the diagram in the question that the resistance has a value,
R=1000ΩR = 1000\Omega
And the capacitance is given as,
C=1×1012FC = 1 \times {10^{ - 12}}F
Therefore, the RHS of the previous equation is the product of the resistance and capacitance. So n doing the product we get,
R×C=1000×1×1012R \times C = 1000 \times 1 \times {10^{ - 12}}
So this gives us a value of,
R×C=109R \times C = {10^{ - 9}}
Therefore, we can substitute this value in the equation and get,
fc1109{f_c} \gg \dfrac{1}{{{{10}^{ - 9}}}}
Hence this becomes,
fc109Hz{f_c} \gg {10^9}Hz
So the carrier frequency should have a suitable value of 109Hz \gg {10^9}Hz

So the correct answer is option C.

Note The carrier frequency is the frequency of the carrier wave that is modulated to transmit signals.
A carrier signal is used for efficient transmission in order to reduce the wavelength. The carrier signal is usually a simple single frequency sinusoid. A detector circuit is used to extract information from a modulated radio frequency current or voltage.