5. A simple electrical circuit consists of a resistor with a resistance R = 10, an inductor with an inductance L = 1 H, a DC power source with a voltage V = 10 volts and a switch S all in series. If the switch S is closed a time t = 0, then from kirchhoffs law the current is governed by the following differential equation. dl L+RI =V dt (a) Using the integrating factor, solve the differential equation to find I as a function of time t. (b) Find the Laplace Transform I(s) of the current I by applying the Laplace transform to the two sides of the differential equation at zero initial conditions, that is I(0) = 0. (c) Solve the differential equation by finding I from its Laplace transform I(s).
5. A simple electrical circuit consists of a resistor with a resistance R = 10, an inductor with an inductance L = 1 H, a DC power source with a voltage V = 10 volts and a switch S all in series. If the switch S is closed a time t = 0, then from kirchhoffs law the current is governed by the following differential equation. dl L+RI =V dt (a) Using the integrating factor, solve the differential equation to find I as a function of time t. (b) Find the Laplace Transform I(s) of the current I by applying the Laplace transform to the two sides of the differential equation at zero initial conditions, that is I(0) = 0. (c) Solve the differential equation by finding I from its Laplace transform I(s).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5.
A simple electrical circuit consists of a resistor with a resistance R = 10, an inductor with an
inductance L = 1 H, a DC power source with a voltage V = 10 volts and a switch S all in
series. If the switch S is closed a timet = 0, then from kirchhoff's law the current is governed
by the following differential equation.
dl
L+RI=V
dt
(a) Using the integrating factor, solve the differential equation to find I as a function
of time t.
(b) Find the Laplace Transform I(s) of the current I by applying the Laplace
transform to the two sides of the differential equation at zero initial conditions,
that is I(0) = 0.
(c) Solve the differential equation by finding I from its Laplace transform I(s).
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