The voltage gain of the amplifier shown below is :

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  1. −(R2/R1)
  2. −(R3/R2
  3. −(R2 || R3)/R
  4. −(R2 + R3)/R1

Answer (Detailed Solution Below)

Option 3 : −(R2 || R3)/R
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Detailed Solution

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Concept:

The given circuit is an inverting amplifier using an operational amplifier (op-amp). In this configuration, the non-inverting terminal is grounded, and input is applied through resistor R1 to the inverting terminal. Resistors R2 and R3 form a voltage divider in the feedback path.

Calculation:

Since R2 and R3 are connected in parallel to ground, their equivalent resistance is:

\( R_f = R_2 \parallel R_3 = \frac{R_2 R_3}{R_2 + R_3} \)

The gain of an inverting amplifier is given by:

\( A_v = -\frac{R_f}{R_1} = -\frac{R_2 \parallel R_3}{R_1} \)

 

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