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Consider a circuit composed of a battery (ɛ= 20 V), a resistor (R = 10 Q) and an inductor (L = 1 mH) all connected in series. Before t=0, the system is in steady state and the current in the circuit i(t) is at its maximum possible value (Imax). At t=0, the battery is removed and replaced by a wire, the circuit then consists in a single loop with the inductor and the resistor in series (no more battery). (a) Find the current in the inductor i(t) as a function of time (provide details on how to find the solution including the exact value of Imax). (b) Do a schematic plot of the current in the inductor as a function of time and calculate the time constant of the system (c) How long will it take for the current i(t) to reach 0.367 (~1/e) of its initial maximal value Imaz ?

Consider a circuit composed of a battery (ɛ= 20 V), a resistor (R = 10 Q) and an inductor (L = 1 mH) all connected in series. Before t=0, the system is in steady state and the current in the circuit i(t) is at its maximum possible value (Imax). At t=0, the battery is removed and replaced by a wire, the circuit then consists in a single loop with the inductor and the resistor in series (no more battery). (a) Find the current in the inductor i(t) as a function of time (provide details on how to find the solution including the exact value of Imax). (b) Do a schematic plot of the current in the inductor as a function of time and calculate the time constant of the system (c) How long will it take for the current i(t) to reach 0.367 (~1/e) of its initial maximal value Imaz ?

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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Please a) to c). Thank you!
Consider a circuit composed of a battery (ɛ= 20 V), a resistor (R = 10 Q) and an inductor (L = 1 mH) all connected in series. Before t=0, the system is in steady state and the current in the circuit i(t) is at its maximum possible value (Imax). At t=0, the battery is removed and replaced by a wire, the circuit then consists in a single loop with the inductor and the resistor in series (no more battery). (a) Find the current in the inductor i(t) as a function of time (provide details on how to find the solution including the exact value of Imax). (b) Do a schematic plot of the current in the inductor as a function of time and calculate the time constant of the system (c) How long will it take for the current i(t) to reach 0.367 (~1/e) of its initial maximal value Imar ?
Transcribed Image Text:Consider a circuit composed of a battery (ɛ= 20 V), a resistor (R = 10 Q) and an inductor (L = 1 mH) all connected in series. Before t=0, the system is in steady state and the current in the circuit i(t) is at its maximum possible value (Imax). At t=0, the battery is removed and replaced by a wire, the circuit then consists in a single loop with the inductor and the resistor in series (no more battery). (a) Find the current in the inductor i(t) as a function of time (provide details on how to find the solution including the exact value of Imax). (b) Do a schematic plot of the current in the inductor as a function of time and calculate the time constant of the system (c) How long will it take for the current i(t) to reach 0.367 (~1/e) of its initial maximal value Imar ?
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