The battery in Exercise 14 is replaced by a generator producing a voltage of E(t) = 12 sin 10t.
(a) Find the charge at time t.
(b) Graph the charge function.
To find : The charge of series RLC circuit at time .
Series RLC circuit with following values.
, , , , and .
Write the expression for differential equation of electric circuit.
Write the expression for general solution with complex roots.
Write the expression for .
Write the expression for auxiliary equation.
Write the expression for differential equation.
Find the differential equation for electric circuit using equation (1).
Substitute for L, for R, for C and for in equation (1),
Modify equation (5) as follows.
Compare equation (6) and (7).
Substitute for a, for b and for in equation (4),
Find the value of .
Simplify as follows.
Compare equations (3) and (8).
Substitute for and for in equation (2),
Modify equation (9) for complementary equation as follows.
Consider the value of as follows.
Differentiate equation (10) with respect to .
Differentiate equation with respect to .
Modify equation (6) as follows.
Substitute for , for and for ,
Compare left hand side (LHS) and right hand side (RHS) of equation
To graph: The charge functions.
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: An Applied Approach (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendental Functions
Finite Mathematics and Applied Calculus (MindTap Course List)
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Probability and Statistics for Engineering and the Sciences
Understanding Basic Statistics
Mathematical Excursions (MindTap Course List)
Mathematical Applications for the Management, Life, and Social Sciences
Elementary Technical Mathematics
Elementary Geometry For College Students, 7e
Single Variable Calculus: Early Transcendentals
Calculus of a Single Variable
Contemporary Mathematics for Business & Consumers
Trigonometry (MindTap Course List)
Elements Of Modern Algebra
Study Guide for Stewart's Multivariable Calculus, 8th
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Calculus: Early Transcendental Functions (MindTap Course List)
Finite Mathematics for the Managerial, Life, and Social Sciences
Elementary Geometry for College Students