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In the given image, we have an op-amp circuit with input voltages \(v_1\) and \(v_2\), and the task is to find the expression for the output voltage \(v_o\) based on these inputs. The problem asks for an expression for \(v_o\) in terms of \(v_1\) and \(v_2\), assuming the operational amplifier is ideal.

### Step-by-step analysis:
- The op-amp configuration is a differential amplifier, which takes the difference between \(v_1\) and \(v_2\) and amplifies it by a factor set by the resistances.
- The formula for the output voltage of a differential amplifier is:
  \[
  v_o = \left( \frac{R_f}{R_1} \right) v_1 - \left( \frac{R_f}{R_2} \right) v_2
  \]
  where:
  - \(R_f\) is the feedback resistor (101 k\(\Omega\)),
  - \(R_1\) is the resistor connected to \(v_1\) (9.9 k\(\Omega\)),
  - \(R_2\) is the resistor connected to \(v_2\) (10.1 k\(\Omega\)).

### Applying the values:
- From the circuit:
  \[
  v_o = \left( \frac{101 \, \text{k}\Omega}{9.9 \, \text{k}\Omega} \right) v_1 - \left( \frac{101 \, \text{k}\Omega}{10.1 \, \text{k}\Omega} \right) v_2
  \]

- Simplifying the ratios:
  \[
  \frac{101}{9.9} \approx 10.202, \quad \frac{101}{10.1} \approx 10.000
  \]

Thus, the output voltage expression becomes:
\[
v_o = 10.202 v_1 - 10.000 v_2
\]

This is the desired expression for the output voltage \(v_o\) in terms of \(v_1\) and \(v_2\).

Would you like me to go into more details or clarify anything? Here are some related questions:

1. How do ideal op-amp assumptions affect the analysis?
2. What happens if we change the feedback resistor value \(R_f\)?
3. Can we express \(v_o\) differently if we use different resistor ratios?
4. How does the input frequency content of \(v_1\) and \(v_2\) affect the output?
5. What are the conditions for stability in such an op-amp circuit?

**Tip:** Always double-check resistor values in differential amplifier circuits, as small differences can significantly affect the output gain.

Given the input voltages v1 and v2 in the op-amp amplifier circuit with resistors, find the expression for the output voltage Vo in terms of v1 and v2. The input voltages are given as v1 = 10 sin(120πt) + 0.25 sin(5000πt) and v2 = 10 sin(120πt) - 0.25 sin(5000πt).

Learn how to calculate the output voltage Vo in a differential amplifier circuit using ideal op-amp assumptions. With input voltages v1 = 10 sin(120πt) + 0.25 sin(5000πt) and v2 = 10 sin(120πt) - 0.25 sin(5000πt), this problem explores the differential amplifier's operation and the effect of resistor ratios on gain.

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