R=6.2 KN +12V R,= 1 KN I. R1= 10 KN v, Vin V2 -12V 1. Write the node equation for the circuit shown, using only the terms Vin, Vo, R1, and R2. 2. Rearrange the equation form part (1) to solve for v/Vin. 3. Replace the resistor values in the expression from part (2) and determine the gain of the op-amp circuit shown.

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Given of what I have hwo do I solve Vo and Vin 

 

### Operational Amplifier Circuit Analysis

**Circuit Diagram:**

- **Input Voltage Source:** \( V_{in} \)
- **Resistors:**
  - \( R_1 = 1 \, \text{k}\Omega \)
  - \( R_2 = 6.2 \, \text{k}\Omega \)
  - \( R_L = 10 \, \text{k}\Omega \)

- **Operational Amplifier (Op-amp) Configuration:**
  - \( +12 \, \text{V} \) connected to the non-inverting terminal.
  - \( -12 \, \text{V} \) connected to the inverting terminal.
  - Inputs: \( v_1 \) and \( v_2 \).
  - Output: \( v_o \).

**Nodes and Currents:**

- \( I_1 \) flows through \( R_1 \).
- \( I_2 \) flows through \( R_2 \).
- \( I \) flows into the non-inverting input.
- \( I_4 \) exits the op-amp to the load resistor \( R_L \).

**Tasks for Analysis:**

1. **Node Equation:**
   - Derive the node equation using the terms \( V_{in}, v_o, R_1, \) and \( R_2 \).

2. **Equation Rearrangement:**
   - Solve the equation from step 1 to express \( v_o/V_{in} \).

3. **Determine Gain:**
   - Use the resistor values from step 2 to determine the gain of the op-amp circuit.

This analysis involves setting up and solving equations based on the given circuit components and configuration to find the operational gain and behavior of the system.
Transcribed Image Text:### Operational Amplifier Circuit Analysis **Circuit Diagram:** - **Input Voltage Source:** \( V_{in} \) - **Resistors:** - \( R_1 = 1 \, \text{k}\Omega \) - \( R_2 = 6.2 \, \text{k}\Omega \) - \( R_L = 10 \, \text{k}\Omega \) - **Operational Amplifier (Op-amp) Configuration:** - \( +12 \, \text{V} \) connected to the non-inverting terminal. - \( -12 \, \text{V} \) connected to the inverting terminal. - Inputs: \( v_1 \) and \( v_2 \). - Output: \( v_o \). **Nodes and Currents:** - \( I_1 \) flows through \( R_1 \). - \( I_2 \) flows through \( R_2 \). - \( I \) flows into the non-inverting input. - \( I_4 \) exits the op-amp to the load resistor \( R_L \). **Tasks for Analysis:** 1. **Node Equation:** - Derive the node equation using the terms \( V_{in}, v_o, R_1, \) and \( R_2 \). 2. **Equation Rearrangement:** - Solve the equation from step 1 to express \( v_o/V_{in} \). 3. **Determine Gain:** - Use the resistor values from step 2 to determine the gain of the op-amp circuit. This analysis involves setting up and solving equations based on the given circuit components and configuration to find the operational gain and behavior of the system.
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