# Op-Amp Resistive Circuit Homework: Finding Vo in a Given Circuit

• Engineering
• sojo
In summary, the problem is to find the voltage drop across the 6k resistor in the given circuit. Using the equation v_out/v_in = (R_1 + R_2)/R_1 and the fact that V+ = V-, the voltage drop can be expressed as V_out = 4V_in. To find V_in, the "conservation of current" law is used to establish V- in terms of V_out and then again to find V+ in terms of V_out and the 4V. This simplifies the problem to two simple resistive voltage dividers in series, making it easier to solve.
sojo

## Homework Statement

The attached picture is the circuit I have been given and I am asked to find Vo (the voltage drop across the 6k resistor.

## Homework Equations

v_out/v_in = (R_1 + R_2)/R_1
V+ = V-

## The Attempt at a Solution

So I know that the voltage drop across the 6k resistor is just the output voltage of the op-amp since there is a ground there.
I used the v_out/v_in = 3+9/3 = 4, so I know V_out = 4V_in
The thing I am having issues with is finding the V_in. I feel like I have 7 unknown currents and I've written out a ton of equations using the KVL and KCL but I feel like I just keep running around in circles with all the unknowns.
Am I going to have to use all the KVL KCL equations to solve this, or is there some simpler method I am missing to find the Vin so I can find the Vout?

#### Attachments

• Screen Shot 2018-10-28 at 9.01.31 PM.png
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sojo said:
v_out/v_in = (R_1 + R_2)/R_1
V+ = V-

You used "conservation of current" to establish V– in terms of Vout. So now you use that same "conservation of current" law to find V+ in terms of Vout and the 4V. The current into the resistor network equals the current that flows from the resistor network.

Just a hint: All you need is the positive feedback factor k+ (setting the 4V dc source equal to zero).
In this case, we have Rp=4k||5k=2.222k and the problem reduces to two simple resistive voltage divider in series.
This shouldn`t be a big problem.

## 1. What is an op-amp resistive circuit?

An op-amp resistive circuit is a type of electrical circuit that utilizes an operational amplifier (op-amp) and resistive elements, such as resistors, to perform mathematical operations like addition, subtraction, and multiplication. It is commonly used in electronic devices and systems, such as amplifiers, filters, and oscillators.

## 2. How does an op-amp resistive circuit work?

An op-amp resistive circuit works by using the properties of an operational amplifier, which is a high-gain voltage amplifier, and resistive elements to manipulate the input signals and produce the desired output. The op-amp amplifies the difference between its two input terminals, and the resistive elements control the amplification and signal processing.

## 3. What are the advantages of using an op-amp resistive circuit?

There are several advantages of using an op-amp resistive circuit, such as high gain, accurate amplification, low noise, and low output impedance. It is also versatile and can be easily configured for various applications. Additionally, op-amp resistive circuits are relatively inexpensive and widely available.

## 4. What are the limitations of an op-amp resistive circuit?

One limitation of an op-amp resistive circuit is that it requires a dual power supply to operate, which can add complexity and cost to the overall system. It is also sensitive to temperature changes and can experience offset voltage and drift. Furthermore, the high gain of the op-amp can lead to instability and oscillation if not properly designed and implemented.

## 5. How can I design an op-amp resistive circuit?

Designing an op-amp resistive circuit involves understanding the circuit's requirements, selecting appropriate op-amp and resistive components, and analyzing the circuit using circuit analysis techniques. There are also various software tools and online resources available to assist in the design process. It is essential to consider factors like stability, noise, and power consumption in the design process to ensure optimal performance of the circuit.

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