Chapter 9.5, Problem 27E

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Chapter
Section

### 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 Â y'+PxÂ y=Q(x), multiply both sides by the integrating factor Â Ix=Â eâˆ«PxdxÂ  and integrate both sides.

2) Given:

Et=40,Â Â L=2H,Â Â R=10Â Î©

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=Â eâˆ«5Â dt=e5t

Multiply the equation by e5t

e5tdIdt+5Ie5t=20e5tâ‡’e5tI

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started