### Problem P10-22: Operational Amplifier Circuit Analysis**Question (d):**What is the time constant \( \tau \) of the response? Plot the response \( v_o(t) \) and give the values of \( v_o \) at \( t = \tau \), \( 2\tau \), and \( 5\tau \).**Circuit Diagram Description:**- **Components:** - **Resistors:** \( R_1 = 10 \, \text{k}\Omega \), \( R_2 = 10 \, \text{k}\Omega \) - **Capacitor:** \( C = 1 \, \mu\text{F} \) - **Operational Amplifier:** Standard op-amp configuration - **Input Voltage Source:** \( v_{\text{in}} = 10 \, \text{V} \)- **Connections:** - The input voltage \( v_{\text{in}} \) is applied across \( R_1 \). - The non-inverting input of the op-amp is connected to ground. - The inverting input of the op-amp is connected to the junction of \( R_2 \) and \( C \). - \( R_2 \) is connected in feedback with the op-amp, forming an RC network with \( C \). - The output voltage \( v_o \) is taken from the op-amp output.**Objective:**- Determine the time constant \( \tau = R_2 \times C \).- Plot \( v_o(t) \) using the calculated \( \tau \).- Calculate and provide \( v_o \) at \( t = \tau \), \( 2\tau \), and \( 5\tau \).### Analysis:- **Time Constant Calculation:** - \( \tau = R_2 \times C = 10 \, \text{k}\Omega \times 1 \, \mu\text{F} = 10 \, \text{ms} \).- **Plot and Calculation:** - Assume the response \( v_o(t) \) follows the standard exponential discharge/charge characteristic due to the RC network. - Utilize the calculated time constant to evaluate \( v_o \) at specific times: \( t = \tau, 2\tau, 5\tau \ ### Problem 10-22:A constant voltage source \( v_{\text{in}}(t) = 10 \) volts is applied to the Op-Amp circuit shown in Fig. P10.22. The output voltage \( v_o(t) \) satisfies the following first-order differential equation and initial conditions:\[ 0.01 \frac{dv_o(t)}{dt} + v_o(t) = -v_{\text{in}}(t), \]\[ v_o(0) = 0 \, \text{V}. \]#### Tasks:(a) Find the transient solution, \( v_{o,\text{tran}}(t) \).(b) Find the steady-state solution \( v_{o,\text{ss}} \) if \( v_{\text{in}} = 10 \, \text{V} \).(c) If the initial output voltage is \( v_o(0) = 0 \, \text{V} \), determine the total response.---**Graph Explanation**: The image shows a problem related to an operational amplifier circuit, focusing on how to solve a differential equation that describes the circuit's behavior. There are no graphs or diagrams present in the image to explain. If there had been a diagram, it would have likely shown the configuration of the operational amplifier circuit.

Answered: (d) What is the time constant r of the…

(d) What is the time constant r of the response? Plot the response v,(1) and give the values of v. at t = t, 2r, and 5r. R = 10 kly ww- C= 1uF R = 10 k2 ww Vcc Vin = 10 V

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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