In the given circuit, the open-loop gain of the op-amp is 15 V/V. What is the closed-loop gain of the given circuit?

In the given circuit, the open-loop gain of the op-amp is 15 V/V. What is the closed-loop gain of the given circuit?

• 1. -2 V/V
• 2. 3 V/V
• 3. 2.5 V/V
• 4. -3.5 V/V

Step-by-Step Solution

Step 1: Identify the circuit.
The circuit is a non-inverting amplifier because the input signal V_i is applied to the non-inverting (+) terminal.

Step 2: Calculate the feedback factor (β).
The feedback factor is the ratio of voltage fed back to the inverting terminal:
β = R₁ / (R₁ + R_f) = 10k / (10k + 20k) = 1/3

Step 3: Apply the finite gain formula.
The closed-loop gain A_CL for a non-ideal op-amp is given by:
A_CL = A_OL / (1 + A_OL × β)
where A_OL = 15.

Step 4: Final calculation.
A_CL = 15 / (1 + 15 × 1/3)
A_CL = 15 / (1 + 5)
A_CL = 15 / 6 = 2.5 V/V

The correct answer is Option 3: 2.5 V/V

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