Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

The figure shows a circuit containing an electrom…

07:16

Question

Answered step-by-step

Problem 28 Easy Difficulty

In the circuit shown in Figure 4, a generator supplies a voltage of $ E(t) = 40 \sin 60t $ volts, the inductance is 1 H, the resistance is $ 20 \Omega, $ and $ I(0) = 1 A. $
(a) Find $ I(t). $
(b) Use a graphing device to draw the graph of the current function.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Pawan Yadav
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Pawan Yadav

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 9

Differential Equations

Section 5

Linear Equations

Related Topics

Differential Equations

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

13:37

Differential Equations - Overview

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Video Thumbnail

33:32

Differential Equations - Example 1

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Join Course
Recommended Videos

04:37

In the circuit shown in Fi…

06:11

In the circuit shown in Fi…

01:13

In the circuit shown in Fi…

04:38

In the circuit shown in Fi…

03:41

In the circuit shown in Fi…

05:37

In the circuit shown in Fi…

03:15

An $L R$ -series circuit h…

01:34

The current through a 40 -…

Watch More Solved Questions in Chapter 9

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38

Video Transcript

turkey Diagram giving is we have a generator e and a resistor r with two arms resistance and in dr within doctrines off to Henry's and they're connected in cities and we have to find current at time T Another condition that is given to us is at time T equals to zero. Uh, current is one MP here and also generate a voltage is 40 times signs 60 t okay. And we have to deal graph that current as well. Okay, To solve this, we need to first convert this equation in tow. Sorry. Can work this graph into equation. So we'll care. Chops law, it shows law. And that says the total drop in voltage across the circuit is equals toe the vaulted supply. Therefore, we'll have easy equals toe drop across the resistor will be awry and drop across in dr will be l. D. I buy deity on substituting values is 40 sign 60 be artist 20 I plus Ellis to Henry's. So that is two times d I buy DP. Okay, now if you write this in standard form, we'll have two times the IBD T plus 20 I is equals to 40 signs 60 t Now we can divide by two so we'll have the a b d t plus 10. I is 20 divided by two so 20 times sign 60 t. Okay, now, if you look at the situation, this is the standard off standard form off linear equation that is divided by D X plus B y equals two Q. So we can calculate integrating factor as a race to integration off P D. X where Peace 10. So erase to integration off 10 D x, which is equals to integration off. Sorry, it is to 10 x right, 10 constant integration of one is X So our solution will be there four eyes it is to 10 x equals two integration off Q times that is 20 sign 60 de times a raise to 10 x d x. Okay, here, twenties constant. So it will come out off integration and we're left with It is to 10 x times sign 60 t. Sorry. This is not okay. So here we don't have the exits. Integrating factor will be here is to integration off PDT. So that is integration off piece tense or 10 DT and that gives us a raise to 10 t So our solution will be eyes that this I times so high times Yeah. Ah, yes, which is it is 2 20 integration off Q I f so Q Is 20 sign 60 d times I f. It is 2 20 DT. Okay, so we can take out 20 since it's a constant value and we'll have integration off sign 60 t it is 2. 20 deity. Okay, so now we can use a formula off integration. So that is integration off areas two x sign b x plus e d x. And it's answer is it is two x or a square plus B square and it's eight times sign Be explicit. See, minus b times cause B X plus e Yeah. Okay, so applying this formula here, we'll have 20 times. It is 2. 20 or what? 60 we have 60. So 60 square is 00 36 Bless 10 square. So that is 100. Then into eight times signed, we explore Asi So is 10 time sign we explosive. That is nothing About 60 de minus b times will be 60 so 60 times cause 60 d Okay, so this is a I plus c. So this is high times here is to 20. Now, if you simplify this, we get 20 over 3700. It is 2. 20. Here it is. 10 times sign 60 T minus 60 times cause 60 t plus c. Okay, so on Cal. Okay, so these are solution for areas to for general solution off, so we can simplify this a little. So this is I times it is 2. 20 equals two. It can cancel this and we can take out 10 from years. This will again become 20/3, 70 years to 20 on this becomes sign 60 be minus six times cause 60 d plus c. Okay, so we can divide by this value since we need value off I So I will be 20 so we can cancel against to over 37. It is 2 20 divided by it is 2. 20. This is science 60 will copy it as it is minus six times cause 60 80 plus c times. If it is divided, it will go in numerator by minus signing power. So that's absolution for I Now we need value off, See to get a particular solution tow. Fourth c were given a T equals to zero eyes, one mbia. Therefore, if you substitute I as one, this two by 37 it is 20 over. We can cancel these two terms so we don't have to write. So this becomes sign 60 times zero minus six times cause zero plus series to it is +20 Okay, so this is I sorry. One because 22 by 37 sign 0 60 time 00 So sign 00 minus called zero is one. So this is minus six plus c. So therefore, value off, see is can write it as one minus too bye. 37 minus six. So it is one plus two. Well, by 37. So on solving this, we get 37 plus 12. So that is 49/37. So that's a value off. See? So our solution is Therefore I particular will be to over 37. Sign 60 t minus six times cause 60 t class to buy. Sorry, it's not too. It's see value. That is 49 by 37 into areas to minus 20. Okay, so this function is two parts the district no metric and exponential, so starting the T value is less the exponential have greater role to play. And we'll have, let's say, a graph like this. But after a time this exponential esti grows, the exponential value becomes very small, enhance This value can be neglected and therefore initially function will start from 49 by 37 will come down and structure weight and then it will settle to a constant amplitude, okay?

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
94
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
54
Hosted by: Alonso M
See More

Related Topics

Differential Equations

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

13:37

Differential Equations - Overview

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Video Thumbnail

33:32

Differential Equations - Example 1

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Join Course
Recommended Videos

04:37

In the circuit shown in Figure $4,$ a generator supplies a voltage of $E(t)=40 …

06:11

In the circuit shown in Figure $4,$ a generator supplies a voltage of $E(t)=40 …

01:13

In the circuit shown in Figure $4,$ a generator supplies a volt- age of $E(t)=…

04:38

In the circuit shown in Figure $4,$ a battery supplies a con- stant voltage of …

03:41

In the circuit shown in Figure $4,$ a battery supplies a constant voltage of 40…

05:37

In the circuit shown in Figure 4, a battery supplies a constant voltage 40 V, t…

03:15

An $L R$ -series circuit has a variable inductor with the inductance defined by…

01:34

The current through a 40 -mH inductor is $$i(t)=\left\{\begin{array}{ll} 0, & t…
Additional Mathematics Questions

03:09

Integration by Partial fraction Evaluate the following functions using parti…

15:12

Tutorial 5
Math 0130
Projectile Motion
A child throws ball upward f…

05:10

The sum of the measures of the angles of parallelogram is 360" In the p…

09:27

Break-Even Analysis Gymnast Clothing manufactures expensive hockey jersey…

01:56

Indicate the following using the picture below
23. The edges are the foll…

07:08

An archieci designs rectangula iowe garden such that the widih arachno-Inira…

01:52

Coum-as
Yalan H
(06.02 MC) Triangle _ ABC is simdar to triangle DEF Us…

02:24

The 68 students in classical music cture class were polled with the results …

11:01

Show R is an equivalence relation and find the distinct equivalence classes:…

01:18

You are performing a right-tailed test with test statistic =1.243, find the …

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started