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Consider the following series RC circuit: Vinlt) Switch 'S' is open at t = . The switch is closed att 0. Let i(t) be the current flowing through the circuit for t0. It is given that input voltage Vin(t) is a unit step input. (a) Describe the dynamics of the system using ordinary differential equation. (b) Derive the transfer function for the system while assuming that initial charge stored in the capacitor is zero. Here, voltage across capacitor is the output. (c) Plot the output of the system with respect to time while assuming time constant to be 1 ms. Assume suitable values of 'R' and 'C'. After achieving a certain value in five time constants, the output almost gets saturated. Estimate the steady-state error. NOTE: Do task (c) analytically and verify your result using computational tool such as MATLAB.

Consider the following series RC circuit: Vinlt) Switch 'S' is open at t = . The switch is closed att 0. Let i(t) be the current flowing through the circuit for t0. It is given that input voltage Vin(t) is a unit step input. (a) Describe the dynamics of the system using ordinary differential equation. (b) Derive the transfer function for the system while assuming that initial charge stored in the capacitor is zero. Here, voltage across capacitor is the output. (c) Plot the output of the system with respect to time while assuming time constant to be 1 ms. Assume suitable values of 'R' and 'C'. After achieving a certain value in five time constants, the output almost gets saturated. Estimate the steady-state error. NOTE: Do task (c) analytically and verify your result using computational tool such as MATLAB.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Consider the following series RC circuit: S. Vinlt) Dut lt) Switch 'S' is open at t . The switch is closed at t = 0. Let i(t) be the current flowing through the circuit for t>0. It is given that input voltage Vin(t) is a unit step input. (a) Describe the dynamics of the system using ordinary differential equation. (b) Derive the transfer function for the system while assuming that initial charge stored in the capacitor is zero. Here, voltage across capacitor is the output. (c) Plot the output of the system with respect to time while assuming time constant to be 1 ms. Assume suitable values of 'R' and 'C'. After achieving a certain value in five time constants, the output almost gets saturated. Estimate the steady-state error. NOTE: Do task (c) analytically and verify your result using computational tool such as MATLAB.
Transcribed Image Text:Consider the following series RC circuit: S. Vinlt) Dut lt) Switch 'S' is open at t . The switch is closed at t = 0. Let i(t) be the current flowing through the circuit for t>0. It is given that input voltage Vin(t) is a unit step input. (a) Describe the dynamics of the system using ordinary differential equation. (b) Derive the transfer function for the system while assuming that initial charge stored in the capacitor is zero. Here, voltage across capacitor is the output. (c) Plot the output of the system with respect to time while assuming time constant to be 1 ms. Assume suitable values of 'R' and 'C'. After achieving a certain value in five time constants, the output almost gets saturated. Estimate the steady-state error. NOTE: Do task (c) analytically and verify your result using computational tool such as MATLAB.
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