Solve Op Amp Circuit Problem: Find V2/V1 w/Potentiometer

[farahtc]

Homework Statement

The op amp circuit shown bellow is intended to provide any gain between -10 (for k=0) and +10 (for k=1) by adjusting the potentiometer. Let R1 and R2 have the scaled values, show that..

V2/V1= {r1/(r1+10k)} [-11/{1+(10kr1/r1+10k)}] + [r2/r2+10(1-k)] [1+ {11/1+10kr1/r1+10k}]

Homework Equations

The Attempt at a Solution

i have no idea how to write nodal equations for a potentiometer. If anyone tell me how to do that, i can figure out the rest by myself. thanks

 

[unplebeian]

Think of the potentiometer as 2 resistors in series with values 10k and 10(1-k). That's all.

 

[piercas]

I would suggest approaching this problem by breaking it down into smaller, more manageable steps. First, we need to understand how a potentiometer works in an op amp circuit. A potentiometer is essentially a variable resistor, with one end connected to a fixed resistor (R2 in this case) and the other end connected to ground. The wiper of the potentiometer can be adjusted to vary the resistance between these two points.

Using this knowledge, we can start by writing the nodal equations for this circuit. The input voltage, V1, is connected to the inverting input of the op amp. The output voltage, V2, is connected to the non-inverting input of the op amp. We can assume that the op amp is in negative feedback, so the voltage at the inverting input will be equal to the voltage at the non-inverting input.

Next, we can consider the different scenarios for the potentiometer. When k=0, the wiper is at the bottom of the potentiometer and the resistance between the wiper and ground is 0. This means that the feedback resistor, R1, is effectively shorted to ground. When k=1, the wiper is at the top of the potentiometer and the resistance between the wiper and ground is equal to the total resistance of the potentiometer (R1+R2). This means that the feedback resistor, R1, is effectively connected in series with R2.

Using these scenarios, we can write the nodal equations for the circuit and solve for V2/V1. I would also recommend using the voltage divider equation to simplify the equations and make them easier to solve.

I hope this helps guide you in the right direction. It's important to break down complex problems into smaller parts and understand the basic principles at play. Good luck with your homework!