Question

The voltage gain of an amplifier with $9\%$ negative feedback is $10$. The voltage gain without feedback will be
$A.100$
$B.90$
$C.10$
$D.1.25$

Answer 1

We can define voltage gain as the ratio of output voltage and input voltage. We should apply the concept and relation between voltage gain with feedback and voltage gain without feedback from the amplifier to solve this particular problem. Amplifier is used to amplify signals.
Formula used:
In this problem we will apply the following simple relation of amplifier,
${{A}_{vf}}=\dfrac{{{A}_{v}}}{1+\beta {{A}_{v}}}$.

Complete answer:
Before calculation we should write down the parameters to be applied in the relation.
${{A}_{vf}}$= Voltage gain with feedback= $10$
${{A}_{v}}$= Voltage gain without feedback=?
$\beta$= Power Amplification= $9\%$
Writing given parameters always helps in solving problems.
Now we will use the following relation between voltage gain with feedback and voltage gain without feedback.
${{A}_{vf}}=\dfrac{{{A}_{v}}}{1+\beta {{A}_{v}}}$
Putting values, we get
$10=\dfrac{{{A}_{v}}}{1+0.09\times {{A}_{v}}}$
$10=\dfrac{{{A}_{v}}}{1+\dfrac{9}{100}{{A}_{v}}}$
Solving further, we get
$10=\dfrac{{{A}_{v}}}{\dfrac{100+9{{A}_{v}}}{100}}$
Further calculation gives,
$10=\dfrac{100{{A}_{v}}}{100+9{{A}_{v}}}$
Simplifying we get,
$1000+90{{A}_{v}}=100{{A}_{v}}$
$10{{A}_{v}}=1000$
${{A}_{v}}=100$

So, the correct answer is “Option A”.

Additional Information:
When a transistor is used to amplify the signal then it is known as the amplifier. Amplification is defined as the process of linearly increasing the amplitude of the signal. An amplifier is used for this vital function. The work of amplification is done by transferring a current from a low to high resistance circuit. There are many configurations of transistors as amplifiers. Common emitter amplifier is one of the types. It should also be noted that an amplifier in feedback in proper phase and magnitude behaves as an oscillator.

Note:
Always, begin to work on these types of problems with basic formulas and then proceed. Identify and relate parameters accordingly. Power amplification is defined as enhancing the level of power of the input signal. Take care whether the parameters are in feedback or without feedback.