Program Explanation Given information: The integral-differential equation for the R L C circuit is written as, L d i d t + R i + 1 C ∫ 0 t i ( τ ) d τ = e ( τ ) The initial values for the above system is given as, i ( 0 ) = 0 The function e ( t ) is defined as, e ( t ) = { 100 sin 10 t 0 ≤ t < π 0 t ≥ π The values for constant L , R and C are defined as, L = 1 R = 0 C = 10 − 4 Calculation: Substitute the function e ( t ) and values of the elements on the integral-differential equation of R L C circuit as shown below. ( 1 ) d i d t + ( 0 ) i + 1 10 − 4 ∫ 0 t i ( τ ) d τ = ( 1 − u ( t − π ) ) 100 sin 10 t d i d t + 10 4 ∫ 0 t i ( τ ) d τ = ( 1 − u ( t − π ) ) 100 sin 10 t d i d t + 10 4 ∫ 0 t i ( τ ) d τ = 100 sin 10 t − 100 u ( t − π ) sin 10 t Take the Laplace transform of R L C circuit integral-differential equation as, L { d i d t + 10 4 ∫ 0 t i ( τ ) d τ } = L { 100 sin 10 t − 100 u ( t − π ) sin 10 t } L { d i d t } + 10 4 L { ∫ 0 t i ( τ ) d τ } = L { 100 sin 10 t } − L { 100 u ( t − π ) sin 10 t } ( s L { i } − i ( 0 ) ) + 10 4 L { i } s = 1000 s 2 + 10 2 − 1000 e − π s s 2 + 10 2 s ( s L { i } − ( 0 ) ) + 10 4 L { i } = 1000 s s 2 + 10 2 − 1000 s

5th Edition

ISBN: 8220100802454

Author: Calvis

Publisher: PEARSON

See similar textbooks

Concept explainers

Rod Cutting

A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

Question

Chapter 7.5, Problem 38P

Program Plan Intro

Program Description: Purpose of the problem is to solve the initial value problem Ldidt+Ri+1C∫0ti(τ)dτ=e(τ);i(0)=0 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.5, Problem 37P

Chapter 7.5, Problem 39P

Students have asked these similar questions

i circled the correct answer could you explain how to get that answer, as well as disprove the other options

the answer is A, could you explain how using STOKE'S theorem

could you explain this pleasethe answer is has sum 1but i dont know how to calculate it

Chapter 7 Solutions

EBK DIFFERENTIAL EQUATIONS

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

Ch. 7.1 - Prob. 11P Ch. 7.1 - Prob. 12P Ch. 7.1 - Prob. 13P Ch. 7.1 - Prob. 14P Ch. 7.1 - Prob. 15P Ch. 7.1 - Prob. 16P Ch. 7.1 - Prob. 17P Ch. 7.1 - Prob. 18P Ch. 7.1 - Prob. 19P Ch. 7.1 - Prob. 20P Ch. 7.1 - Prob. 21P Ch. 7.1 - Prob. 22P Ch. 7.1 - Prob. 23P Ch. 7.1 - Prob. 24P Ch. 7.1 - Prob. 25P Ch. 7.1 - Prob. 26P Ch. 7.1 - Prob. 27P Ch. 7.1 - Prob. 28P Ch. 7.1 - Prob. 29P Ch. 7.1 - Prob. 30P Ch. 7.1 - Prob. 31P Ch. 7.1 - Prob. 32P Ch. 7.1 - Prob. 33P Ch. 7.1 - Prob. 34P Ch. 7.1 - Prob. 35P Ch. 7.1 - Prob. 36P Ch. 7.1 - Given a0, let f(t)=1 if 0__1a,f(t)=0 if t__a....Ch. 7.1 - Given that 0ab. Let f(t)=1 if a__tb,f(t)=0 if...Ch. 7.1 - Prob. 39P Ch. 7.1 - Prob. 40P Ch. 7.1 - Prob. 41P Ch. 7.1 - Given constants a and b. define h(t) for t__0 by...Ch. 7.2 - Prob. 1P Ch. 7.2 - Prob. 2P Ch. 7.2 - Prob. 3P Ch. 7.2 - Prob. 4P Ch. 7.2 - Prob. 5P Ch. 7.2 - Prob. 6P Ch. 7.2 - Prob. 7P Ch. 7.2 - Prob. 8P Ch. 7.2 - Prob. 9P Ch. 7.2 - Prob. 10P Ch. 7.2 - Prob. 11P Ch. 7.2 - Prob. 12P Ch. 7.2 - Prob. 13P Ch. 7.2 - Prob. 14P Ch. 7.2 - Prob. 15P Ch. 7.2 - Prob. 16P Ch. 7.2 - Prob. 17P Ch. 7.2 - Prob. 18P Ch. 7.2 - Prob. 19P Ch. 7.2 - Prob. 20P Ch. 7.2 - Prob. 21P Ch. 7.2 - Prob. 22P Ch. 7.2 - Prob. 23P Ch. 7.2 - Prob. 24P Ch. 7.2 - Prob. 25P Ch. 7.2 - Prob. 26P Ch. 7.2 - Prob. 27P Ch. 7.2 - Prob. 28P Ch. 7.2 - Prob. 29P Ch. 7.2 - Prob. 30P Ch. 7.2 - Prob. 31P Ch. 7.2 - Prob. 32P Ch. 7.2 - Prob. 33P Ch. 7.2 - Prob. 34P Ch. 7.2 - Prob. 35P Ch. 7.2 - Prob. 36P Ch. 7.2 - Prob. 37P Ch. 7.3 - Prob. 1P Ch. 7.3 - Prob. 2P Ch. 7.3 - Prob. 3P Ch. 7.3 - Prob. 4P Ch. 7.3 - Prob. 5P Ch. 7.3 - Prob. 6P Ch. 7.3 - Prob. 7P Ch. 7.3 - Prob. 8P Ch. 7.3 - Prob. 9P Ch. 7.3 - Prob. 10P Ch. 7.3 - Prob. 11P Ch. 7.3 - Prob. 12P Ch. 7.3 - Prob. 13P Ch. 7.3 - Prob. 14P Ch. 7.3 - Prob. 15P Ch. 7.3 - Prob. 16P Ch. 7.3 - Prob. 17P Ch. 7.3 - Prob. 18P Ch. 7.3 - Prob. 19P Ch. 7.3 - Prob. 20P Ch. 7.3 - Prob. 21P Ch. 7.3 - Prob. 22P Ch. 7.3 - Prob. 23P Ch. 7.3 - Prob. 24P Ch. 7.3 - Prob. 25P Ch. 7.3 - Prob. 26P Ch. 7.3 - Prob. 27P Ch. 7.3 - Prob. 28P Ch. 7.3 - Prob. 29P Ch. 7.3 - Prob. 30P Ch. 7.3 - Prob. 31P Ch. 7.3 - Prob. 32P Ch. 7.3 - Prob. 33P Ch. 7.3 - Prob. 34P Ch. 7.3 - Prob. 35P Ch. 7.3 - Prob. 36P Ch. 7.3 - Prob. 37P Ch. 7.3 - Prob. 38P Ch. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.4 - Find the convolution f(t)g(t) in Problems 1...Ch. 7.4 - Prob. 2P Ch. 7.4 - Prob. 3P Ch. 7.4 - Prob. 4P Ch. 7.4 - Prob. 5P Ch. 7.4 - Prob. 6P Ch. 7.4 - Prob. 7P Ch. 7.4 - Prob. 8P Ch. 7.4 - Prob. 9P Ch. 7.4 - Prob. 10P Ch. 7.4 - Prob. 11P Ch. 7.4 - Prob. 12P Ch. 7.4 - Prob. 13P Ch. 7.4 - Prob. 14P Ch. 7.4 - Prob. 15P Ch. 7.4 - Prob. 16P Ch. 7.4 - Prob. 17P Ch. 7.4 - Prob. 18P Ch. 7.4 - Prob. 19P Ch. 7.4 - Prob. 20P Ch. 7.4 - Prob. 21P Ch. 7.4 - Prob. 22P Ch. 7.4 - Prob. 23P Ch. 7.4 - Prob. 24P Ch. 7.4 - Prob. 25P Ch. 7.4 - Prob. 26P Ch. 7.4 - Prob. 27P Ch. 7.4 - Prob. 28P Ch. 7.4 - Prob. 29P Ch. 7.4 - Prob. 30P Ch. 7.4 - Prob. 31P Ch. 7.4 - Prob. 32P Ch. 7.4 - Prob. 33P Ch. 7.4 - Prob. 34P Ch. 7.4 - Prob. 35P Ch. 7.4 - Prob. 36P Ch. 7.4 - Prob. 37P Ch. 7.4 - Prob. 38P Ch. 7.4 - Prob. 39P Ch. 7.4 - Prob. 40P Ch. 7.4 - Prob. 41P Ch. 7.5 - Prob. 1P Ch. 7.5 - Prob. 2P Ch. 7.5 - Prob. 3P Ch. 7.5 - Prob. 4P Ch. 7.5 - Prob. 5P Ch. 7.5 - Prob. 6P Ch. 7.5 - Prob. 7P Ch. 7.5 - Prob. 8P Ch. 7.5 - Prob. 9P Ch. 7.5 - Prob. 10P Ch. 7.5 - Prob. 11P Ch. 7.5 - Prob. 12P Ch. 7.5 - Prob. 13P Ch. 7.5 - Prob. 14P Ch. 7.5 - Prob. 15P Ch. 7.5 - Prob. 16P Ch. 7.5 - Prob. 17P Ch. 7.5 - Prob. 18P Ch. 7.5 - Prob. 19P Ch. 7.5 - Prob. 20P Ch. 7.5 - Prob. 21P Ch. 7.5 - Prob. 22P Ch. 7.5 - Prob. 23P Ch. 7.5 - Prob. 24P Ch. 7.5 - Prob. 25P Ch. 7.5 - Prob. 26P Ch. 7.5 - Let g(t) be the staircase function of Fig. 7.5.15....Ch. 7.5 - Suppose that f(i) is a periodic function of period...Ch. 7.5 - Suppose that f(t) is the half-wave rectification...Ch. 7.5 - Let g(t)=u(tk)f(tk), where f(t) is the function of...Ch. 7.5 - Prob. 31P Ch. 7.5 - Prob. 32P Ch. 7.5 - Prob. 33P Ch. 7.5 - Prob. 34P Ch. 7.5 - Prob. 35P Ch. 7.5 - Prob. 36P Ch. 7.5 - Prob. 37P Ch. 7.5 - Prob. 38P Ch. 7.5 - Prob. 39P Ch. 7.5 - Prob. 40P Ch. 7.5 - Prob. 41P Ch. 7.5 - Prob. 42P Ch. 7.6 - Prob. 1P Ch. 7.6 - Prob. 2P Ch. 7.6 - Prob. 3P Ch. 7.6 - Prob. 4P Ch. 7.6 - Prob. 5P Ch. 7.6 - Prob. 6P Ch. 7.6 - Prob. 7P Ch. 7.6 - Prob. 8P Ch. 7.6 - Prob. 9P Ch. 7.6 - Prob. 10P Ch. 7.6 - Prob. 11P Ch. 7.6 - Prob. 12P Ch. 7.6 - Prob. 13P Ch. 7.6 - Prob. 14P Ch. 7.6 - This problem deals with a mass in on a spring...Ch. 7.6 - Prob. 16P Ch. 7.6 - Prob. 17P Ch. 7.6 - Prob. 18P Ch. 7.6 - Prob. 19P Ch. 7.6 - Repeat Problem 19, except suppose that the switch...Ch. 7.6 - Prob. 21P Ch. 7.6 - Prob. 22P

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Program Description: Purpose of the problem is to solve the initial value problem L d i d t + R i + 1 C ∫ 0 t i ( τ ) d τ = e ( τ ) ; i ( 0 ) = 0 .

Solution Summary: The author explains the function e(t) and values of the elements on the integral-differential equation of RLC circuit.

Concept explainers

Program Description: Purpose of the problem is to solve the initial value problem Ldidt+Ri+1C∫0ti(τ)dτ=e(τ);i(0)=0 .

Want to see the full answer?

Chapter 7 Solutions