What is the output voltage (Vout) of the given op-amp circuit?

Steps to Solve

1. Identifying the Circuit Configuration

The circuit consists of a non-inverting op-amp configuration. The non-inverting input is connected to a voltage divider formed by two resistors.

2. Calculating the Non-Inverting Input Voltage ($V_+$)

To find the non-inverting input voltage $V_+$, use the voltage divider formula:

$$ V_+ = \frac{R_2}{R_1 + R_2} \times V_{in} $$

Here, resistor values are:

• $R_1 = 1 , kΩ$ (between 2V and $V_+$)
• $R_2 = 1 , kΩ$ (between 3V and $V_+$)
• $V_{in} = 2V$ (top voltage)

Calculate $V_+$ by considering the voltage at the non-inverting input:

$$ V_+ = \frac{1kΩ}{1kΩ + 1kΩ} \times (2V - 3V) + 3V = \frac{1}{2}(-1) + 3 = 2.5V $$

3. Calculating the Inverting Input Voltage ($V_-$)

Use the voltage divider again for the inverting input voltage $V_-$. The input voltage is the output voltage $V_{out}$ and we consider the feedback from the output through the $5kΩ$ resistor:

$$ V_- = \frac{V_{out}}{5kΩ + 8kΩ} \cdot 8kΩ $$

4. Setting Up the Feedback Loop

In a proper op-amp operation (assuming ideal), $V_+ \approx V_-$. Therefore, set the two equations equal to each other:

$$ 2.5V = \frac{V_{out}}{5kΩ + 8kΩ} \cdot 8kΩ $$

Solve for $V_{out}$:

$$ V_{out} = 2.5V \cdot \frac{5kΩ + 8kΩ}{8kΩ} $$

5. Calculating the Final Output Voltage ($V_{out}$)

Substituting, we have:

$$ V_{out} = 2.5V \cdot \frac{13kΩ}{8kΩ} $$

6. Final Calculation

Now perform the final multiplication:

$$ V_{out} = 2.5V \cdot 1.625 = 4.0625V $$