# CIRCUIT ANALYSIS: 8 Resistors, 1 IVS, 1 Differential Op-Amp - Find Vo

• VinnyCee
In summary, the conversation is about finding V_0 in a differential amplifier circuit driven by a bridge. The process involves using Ideal Op-Amp relationships and KCL to solve for V_2, V_3, V_4, and V_0. The final answer for V_0 is 4.363mV. The expert suggests using linear algebra instead of substitutions for a cleaner solution.

## Homework Statement

The circuit below is a differential amplifier driven by a bridge, find $V_0$.

http://img476.imageshack.us/img476/8827/chapter5problem48fi2.jpg [Broken]

## Homework Equations

KCL, v = i R, Ideal Op-Amp relationships

## The Attempt at a Solution

http://img259.imageshack.us/img259/8314/chapter5problem48part2fs0.jpg [Broken]

By the Ideal Op-Amp relationships, we know that there is 0 current at both input terminals of the Op-Amp.

KCL at $V_2$)

$$\frac{0.005\,-\,V_2}{40000}\,=\,\frac{V_2}{60000}\,+\,\frac{V_2\,-\,V_4}{20000}$$

$$18\,V_2\,-\,12\,V_4\,=\,0.003$$ < ------ Equation 1

KCL at $V_4$)

$$\frac{V_2\,-\,V_4}{20000}\,=\,\frac{V_4}{80000}$$

$$4\,V_2\,-\,5\,V_4\,=\,0$$ <----- Equation 2

Now, using equations 1 and 2, I get $V_2\,=\,0.003571\,V$ and $V_4\,=\,0.002857\,V$. Does that seem right?

By the relationships of an ideal Op-Amp, $V_3\,=\,V_4$, so $V_3\,=\,0.002857\,V$.

KCL at $V_1$)

$$\frac{0.005\,-\,V_1}{10000}\,=\,\frac{V_1}{30000}\,+\,\frac{V_1\,-\,V_3}{20000}$$

$$11\,V_1\,-\,3\,V_3\,=\,0.03$$ <----- Equation 3

KCL at $V_3$)

$$\frac{V-1\,-\,V_3}{20000}\,=\,\frac{V_3\,-\,V_0}{80000}$$

$$4\,V_1\,-\,3\,V_3\,+\,V_0\,=\,0$$ <----- Equation 4

Using equations 3 and 4, I get $V_0\,=\,0.004363\,V$.

$$V_0\,=\,4.363\,mV$$ <------ Is that right?

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Bump - Bump:)

Looks good. Quick question though, why don't you use linear algebra instead of messy substitutions?

## 1. What is circuit analysis?

Circuit analysis is the process of studying and understanding the behavior of electrical circuits. This involves using various mathematical and analytical techniques to analyze the flow of current, voltage, and power within a circuit.

## 2. What are resistors and how do they affect a circuit?

Resistors are passive electrical components that impede the flow of current within a circuit. They are used to control the amount of current and voltage within a circuit, and their value is measured in ohms. In the context of this circuit, the 8 resistors are likely being used to divide the input voltage and create a specific output voltage.

## 3. What is an IVS in this circuit analysis?

An IVS, or independent voltage source, is a source of electrical energy that maintains a constant voltage regardless of the current flowing through it. In this circuit, the IVS is likely providing a known input voltage for analysis.

## 4. What is a differential op-amp and how does it work in this circuit?

A differential op-amp is a type of amplifier that amplifies the difference between two input voltages. In this circuit, it is likely being used to amplify the voltage difference between the input voltage from the IVS and the output voltage, Vo. This allows for precise measurement and control of the output voltage.

## 5. How do I find the value of Vo in this circuit?

To find the value of Vo, you can use the equation Vout = (Rf/Rin) * Vin, where Rf is the feedback resistor and Rin is the input resistor of the op-amp. By substituting the known values and solving for Vo, you can determine the output voltage of the circuit.