Math Problem Statement

Calculate v_0 in the circuit of Figure 1.

Solution

The circuit shown in your image is an op-amp circuit with resistors and a current source. We are tasked with calculating the output voltage v0v_0 at the output of the operational amplifier.

Analyzing the circuit:

  1. Current Source: A 5 mA current source is connected in parallel with a 5 kΩ resistor. This branch is connected to the negative input of the op-amp through a 20 kΩ resistor.

  2. Op-Amp Configuration: The operational amplifier is in a negative feedback configuration, as there is a resistor of 10 kΩ connected between the output and the inverting input. The non-inverting input is grounded, which makes this a non-inverting amplifier.

Steps to solve:

  • Since the non-inverting terminal of the op-amp is connected to ground (0V), the voltage at the inverting terminal, v1v_1, will also be approximately 0V (virtual short circuit in ideal op-amp conditions).

  • Applying Kirchhoff's Current Law (KCL) at the inverting terminal: v1v010kΩ+v1vin20kΩ=0\frac{v_1 - v_0}{10\,k\Omega} + \frac{v_1 - v_{in}}{20\,k\Omega} = 0 where vinv_{in} is the voltage across the 5 kΩ resistor due to the 5 mA current source.

Let me calculate these values for you.The output voltage v0v_0 of the circuit is 12.5V-12.5 \, \text{V}.

Would you like more details on the steps or have any other questions?

Here are some related questions for further exploration:

  1. How does the virtual short principle in op-amps work?
  2. What happens if the feedback resistor values are changed?
  3. Can you explain Kirchhoff's Current Law (KCL) in more detail?
  4. How would the circuit behave with a non-ideal op-amp?
  5. What is the significance of the negative sign in the output voltage?

Tip: In op-amp circuits, the output voltage is often influenced by the ratio of feedback resistors.

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Math Problem Analysis

Mathematical Concepts

Electrical Circuit Analysis
Operational Amplifiers
Kirchhoff's Current Law

Formulas

I = V / R
KCL: ΣI_in = ΣI_out

Theorems

Kirchhoff's Current Law (KCL)
Virtual Short Principle in Ideal Op-Amps

Suitable Grade Level

Undergraduate Electrical Engineering