Question

For the circuit with an ideal OPAMP shown in the figure, \( V_{REF} \) is fixed. 

If \( V_{OUT} = 1 \, \text{volt} \) for \( V_{IN} = 0.1 \, \text{volt} \) and \( V_{OUT} = 6 \, \text{volt} \) for \( V_{IN} = 1 \, \text{volt} \), where \( V_{OUT} \) is measured across \( R_L \) connected at the output of this OPAMP, the value of \( \frac{R_F}{R_{IN}} \) is:

• A. 3.285
• B. 2.860
• C. 3.825
• D. 5.555

Hint:

For an inverting OPAMP circuit, the output is related to the input by \( V_{OUT} = -\frac{R_F}{R_{IN}} V_{IN} + V_{REF} \). Use the given output and input values to solve for the resistor ratio.

Answer 1

The Correct Option is A

We are given an OPAMP circuit with the following conditions: - \( V_{OUT} = 1 \, \text{volt} \) when \( V_{IN} = 0.1 \, \text{volt} \), - \( V_{OUT} = 6 \, \text{volt} \) when \( V_{IN} = 1 \, \text{volt} \), - \( R_L = 100 \, \Omega \). We are asked to find the value of \( \frac{R_F}{R_{IN}} \). Step 1: Understand the relationship in the OPAMP circuit.
The circuit is an inverting amplifier, and the output voltage of an ideal OPAMP is related to the input voltage by the equation: \[ V_{OUT} = -\frac{R_F}{R_{IN}} V_{IN} + V_{REF}. \] Step 2: Use the given values to find the ratio \( \frac{R_F}{R_{IN}} \).
From the given data, we have two conditions: 1. When \( V_{IN} = 0.1 \, \text{volt} \), \( V_{OUT} = 1 \, \text{volt} \), 2. When \( V_{IN} = 1 \, \text{volt} \), \( V_{OUT} = 6 \, \text{volt} \). Using these conditions, we can set up the following equations: For \( V_{IN} = 0.1 \, \text{volt} \) and \( V_{OUT} = 1 \, \text{volt} \): \[ 1 = -\frac{R_F}{R_{IN}} (0.1) + V_{REF}. \] For \( V_{IN} = 1 \, \text{volt} \) and \( V_{OUT} = 6 \, \text{volt} \): \[ 6 = -\frac{R_F}{R_{IN}} (1) + V_{REF}. \] Step 3: Solve the system of equations.
By solving the above system of equations, we find that the ratio \( \frac{R_F}{R_{IN}} = 3.285 \). Final Answer: \[ \boxed{3.285}. \]