Question

An amplifier has a voltage gain \[{A_{\text{v}}} = 1000\] . The voltage gain in \[{\text{dB}}\] is:
A. \[{\text{30}}\,{\text{dB}}\]
B. \[{\text{60}}\,{\text{dB}}\]
C. \[{\text{3}}\,{\text{dB}}\]
D. \[{\text{20}}\,{\text{dB}}\]

Answer 1

Hint: First of all, we will use the formula which relates voltage gain in \[{\text{dB}}\] to the voltage gain \[{A_{\text{v}}}\] . We will substitute the required values and manipulate accordingly to obtain the result.

Complete step by step answer:In the given question, we are supplied with the following data:
The voltage gain of an amplifier is \[1000\] i.e. \[{A_{\text{v}}} = 1000\] .
We are asked to find the voltage gain in \[{\text{dB}}\] .

To begin with, we know a formula, which gives the voltage gain in \[{\text{dB}}\] , which is given below:
\[A = 10\log {A_{\text{v}}}\] …… (1)
Where,
\[A\] indicates the voltage gain in \[{\text{dB}}\] .
\[{A_{\text{v}}}\] indicates the voltage gain.

Now, by substituting the required values in the equation (1), we get:
\[
\Rightarrow A = 10\log {A_{\text{v}}} \\
\Rightarrow A = 10 \times \log 1000 \\
\Rightarrow A = 10 \times \log {10^3} \\
\Rightarrow A = 10 \times 3 \\
\]
Again, multiplying we get the answer:
\[\Rightarrow A = 30\,{\text{dB}}\]

Hence, the voltage gain in \[{\text{dB}}\] is \[30\,{\text{dB}}\]. The correct option is A.

Additional information:
An amplifier, an electronic amplifier or a (informal) amplifier is an electronic system which can increase the signal power (a voltage or current that changes over time). The amount of amplification that an amplifier produces is determined by its gain: the ratio of output voltage, current, or input power. A circuit that has a power gain greater than one is an amplifier. Either a different piece of equipment or an electric circuit located inside another system may be an amplifier.

Note:While solving this problem, many students seem to have a confusion regarding the logarithm part, which clearly states that it is of base \[10\] , rather than base \[e\] . Taking the logarithm with base \[e\] may deviate the calculated result from the actual one.