Question

The voltage gain in the following amplifier is:

A: 10
B: 100
C: 1000
D: 9.9

Answer 1

Hint:In the given question, we are given an op-amp or an operational amplifier circuit. We can use the formula for voltage gain in op-amp and deduce the values from the given values. The earthed parts are to be noted for calculation.

Formulas used:
Voltage gain of amplifier${{A}_{V}}=\dfrac{{{V}_{0}}}{{{V}_{i}}}$ , or this can be interpreted as the ratio between the input voltage and the output voltage of the circuit.

Complete step by step answer:
Gain is termed as measure of how the given amplifier can amplify the input signal, or the factor with which the increased output is generated.Here, the voltage gain is the ratio between the output voltage and the input voltage.From our circuit, we find that the alternating input voltage is ${{V}_{i}}$.The path with the $10K\Omega $ resistor is earthed. Hence, the voltage there would be zero.By virtual grounding, the point at the negative terminal of the op amp would also be zero. Hence the current I choose the path with the $100K\Omega $resistor.Hence the output is collected here.
${{A}_{V}}=\dfrac{{{V}_{0}}}{{{V}_{i}}}=\dfrac{i{{R}_{0}}}{i{{R}_{i}}}=\dfrac{100k\Omega }{1k\Omega }=100$

Hence, the value of the voltage gain is 100.Therefore, option B is the correct answer among the given options.

Note:Sometimes when this circuit is given, we might be asked to find the feedback resistance or this term might get used somewhere. It is nothing but the resistance at which the output is collected. Its value determines the overall gain. Hence, students must familiarize themselves with this term.