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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

In the circuit shown in Figure 4, a battery supplies a constant voltage of 40 V, the inductance is 2 H, the resistance is 10 Ω , and I ( 0 ) = 0

(a) Find I ( t ) .

(b) Find the current after 0.1 seconds.

To determine

To find:

It

Explanation

1) Concept:

To solve the linear differential equation  y'+Px y=Q(x), multiply both sides by the integrating factor  Ix= ePxdx  and integrate both sides.

2) Given:

Et=40,  L=2H,  R=10 Ω

3) Calculation:

The differential equation for the circuit as shown in figure is

LdIdt+RI=E(t)

Substitute the given values.

2dIdt+10I=40

Divide both sides by 2

dIdt+5I=20

Using the concept, find the integrating factor.

Ix= e5 dt=e5t

Multiply the equation by e5t

e5tdIdt+5Ie5t=20e5te5tI

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