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Consider the circuit shown below left. ww 100 Ω 5 V SW1 500 mH ww 100 02 ww Rth Vth SW1 a ell 500 mH a. The switch and inductor can viewed as being attached to Thevenin equivalent circuit shown (above right). Show that Vth=2.5V and Rth=50 2. b. Derive the governing equation for the inductor current using KVL and state the initial condition. c. Solve the governing equation to determine the current through the inductor with time if the switch is closed at t=0. d. What is the time constant t for the circuit? What is the current at t=t? e. Plot the current across the inductor vs. time. f. Plot the voltage across the inductor vs. time.

Consider the circuit shown below left. ww 100 Ω 5 V SW1 500 mH ww 100 02 ww Rth Vth SW1 a ell 500 mH a. The switch and inductor can viewed as being attached to Thevenin equivalent circuit shown (above right). Show that Vth=2.5V and Rth=50 2. b. Derive the governing equation for the inductor current using KVL and state the initial condition. c. Solve the governing equation to determine the current through the inductor with time if the switch is closed at t=0. d. What is the time constant t for the circuit? What is the current at t=t? e. Plot the current across the inductor vs. time. f. Plot the voltage across the inductor vs. time.

Introductory Circuit Analysis (13th Edition)
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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Can you do b-d please. I’m not understanding that
**Circuit Analysis Problem:** **Circuit Description:** - **Left Circuit:** - Voltage Source: 5 V - Resistors: Two 100 Ω resistors - Inductor: 500 mH - Switch (SW1): Controls the connection of the circuit - **Right Circuit (Thevenin Equivalent):** - Thevenin Voltage (\(V_{th}\)) - Thevenin Resistance (\(R_{th}\)) - Inductor: 500 mH - Switch (SW1): Controls the connection **Tasks:** a. Analyze the circuit to verify that the Thevenin equivalent voltage \(V_{th}\) is 2.5 V and the Thevenin resistance \(R_{th}\) is 50 Ω. b. Derive the governing equation for the inductor current using Kirchhoff's Voltage Law (KVL). State the initial condition of the circuit. c. Solve the governing equation to determine the current through the inductor as a function of time when the switch is closed at \(t=0\). d. Calculate the time constant (\(\tau\)) for the circuit and determine the current at \(t=\tau\). e. Plot the current across the inductor versus time. f. Plot the voltage across the inductor versus time. This problem involves applying circuit analysis techniques, including the use of Thevenin's theorem, KVL, and transient analysis to explore the behavior of the inductor in response to switching actions.
Transcribed Image Text:**Circuit Analysis Problem:** **Circuit Description:** - **Left Circuit:** - Voltage Source: 5 V - Resistors: Two 100 Ω resistors - Inductor: 500 mH - Switch (SW1): Controls the connection of the circuit - **Right Circuit (Thevenin Equivalent):** - Thevenin Voltage (\(V_{th}\)) - Thevenin Resistance (\(R_{th}\)) - Inductor: 500 mH - Switch (SW1): Controls the connection **Tasks:** a. Analyze the circuit to verify that the Thevenin equivalent voltage \(V_{th}\) is 2.5 V and the Thevenin resistance \(R_{th}\) is 50 Ω. b. Derive the governing equation for the inductor current using Kirchhoff's Voltage Law (KVL). State the initial condition of the circuit. c. Solve the governing equation to determine the current through the inductor as a function of time when the switch is closed at \(t=0\). d. Calculate the time constant (\(\tau\)) for the circuit and determine the current at \(t=\tau\). e. Plot the current across the inductor versus time. f. Plot the voltage across the inductor versus time. This problem involves applying circuit analysis techniques, including the use of Thevenin's theorem, KVL, and transient analysis to explore the behavior of the inductor in response to switching actions.
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