Electric Circuit The diagram shows a simple electric circuit consisting of a power source, a
resistor, and an inductor.
A model of the current I, in amperes (A) at time t is given by the first-order differential equation
where E(t) is the voltage (V) produced by the power source, R is the resistance, in ohms and
is the inductance, in henrys (H). Suppose the electric circuit consists of a 24-V power source, a
12- 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.
To Graph: A slope field for the given differential equation.
, where , and inductor.
Using the differential equation …… (1)
It is found that
The slope field is plotted below using a graphing utility desmos tool
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