Vb Vb dI R + I L dt L eeeeeee (a) Show that when the switch S is closed, the time-dependence of the current is governed by the following first-order differential equation: = L (b) Follow the methods used in class to solve this differential equation and find an expression for I(t). Assume that the switch is closed at time t = 0 and I(0) = 0. For the RC circuit, the relevant charging time constant was 7 = RC. What is the time constant that determines how the current increases after the switch is closed? (c) What is the time dependence of the voltage across the inductor after the switch is closed? (d) Sketch I(t) and V₁(t) as a function of time. Indicate the maximum values of I and V₁ and their values when t = 7 where 7 is the time constant you found in part (b).

Vb Vb dI R + I L dt L eeeeeee (a) Show that when the switch S is closed, the time-dependence of the current is governed by the following first-order differential equation: = L (b) Follow the methods used in class to solve this differential equation and find an expression for I(t). Assume that the switch is closed at time t = 0 and I(0) = 0. For the RC circuit, the relevant charging time constant was 7 = RC. What is the time constant that determines how the current increases after the switch is closed? (c) What is the time dependence of the voltage across the inductor after the switch is closed? (d) Sketch I(t) and V₁(t) as a function of time. Indicate the maximum values of I and V₁ and their values when t = 7 where 7 is the time constant you found in part (b).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Voltage Across Inductor

An actor is a passive electrical component that consists of a coil bent in the form of wire which uses electromagnetism to produce electric current through the coil. When the electric current flows through a conductor that is the coil, a magnetic flux is developed around the conductor. This flow of current through the coil creates a magnetic field based on Fleming's Right-hand thumb rule. If there is any decrease in the current passing through the inductor, then the magnetic field will also decrease and energy is released through the generation of electric current. There is also a secondary voltage inducing in the same coil due to the magnetic flux, since it opposes any changes in the electric current flowing through the circuit. An inductor is also called choke, coil, or solenoid. A choke is designed to block certain frequencies when the DC current passes. A winding coil is coated with insulation to give extra insulation and protect the circuit. They are usually tightly wrapped around a central core which is cylindrical in nature so that the magnetic flux can be induced. The solenoid is a three-dimension coil that is used to exhibit electromagnetism when the magnetic field is developed due to the current flowing through the coil. The sign convention of the inductor is the same as the power dissipating device. When the current flows into the positive side of the voltage across the inductor, the value is positive and the inductor dissipates power whereas when the inductor releases the power back to the circuit, the current has a negative sign convention. 

Question

Vb
S
R
ooooooo
Vb dI R
= + I
dt L
L
L
(a) Show that when the switch S is closed, the time-dependence of the current is governed by the
following first-order differential equation:
(b) Follow the methods used in class to solve this differential equation and find an expression for
I(t). Assume that the switch is closed at time t = 0 and I(0) = 0. For the RC circuit, the relevant
charging time constant was 7 = RC. What is the time constant that determines how the current
increases after the switch is closed?
(c) What is the time dependence of the voltage across the inductor after the switch is closed?
(d) Sketch I(t) and V₁ (t) as a function of time. Indicate the maximum values of I and V₁ and their
values when t = 7 where 7 is the time constant you found in part (b).

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