   Chapter 6.1, Problem 91E

Chapter
Section
Textbook Problem

Electric Circuit The diagram shows a simple electric circuit consisting of a power source, aresistor, and an inductor. A model of the current I, in amperes (A) at time t is given by the first-order differential equation L d I d t + R I = E ( t ) where E(t) is the voltage (V) produced by the power source, R is the resistance, in ohms Ω andis the inductance, in henrys (H). Suppose the electric circuit consists of a 24-V power source, a12- resistor, and a 4-H inductor.(a) Sketch a slope field for the differential equation.(b) What is the limiting value of the current? Explain.

a)

To determine

To Graph: A slope field for the given differential equation.

Explanation

Given:

LdIdt+RI=E(t), where E(t) =24V, R =12Ω and L =4H inductor.

Graph:

Using the differential equation LdIdt+RI=E(t) …… (1)

It is found that

4dIdt+12I=24dIdt=63I

The slope field is plotted below using a graphing utility desmos tool

b)

To determine
The limiting value of the current.

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