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Solved: Find the charge on the capacitor and the current

A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill ISBN: 9781111827052 44

Solution for problem 56E Chapter 5.1

A First Course in Differential Equations with Modeling Applications | 10th Edition

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A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill

A First Course in Differential Equations with Modeling Applications | 10th Edition

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Problem 56E

Find the charge on the capacitor and the current in an LC circuit when L = 0.1 h, C = 0.1 f, E(t) = 100 sin ?t V, q(0) = 0 C, and i(0) = 0 A.

Step-by-Step Solution:
Step 1 of 3

Solution:Step-1:In this problem we need to find the charge on the capacitor and the current in an LC circuit when .Step-2:We know that,………..(1)Where, We know that, the relation between voltage and current in circuit analysis is .represents the voltage drop across the inductor.represents the voltage drop across the resistor.represents the voltage drop across the capacitor.Given,.Substitute these values in equation (1) we get.…………(2).Step-3:Now the auxiliary equation of the differential equation is :Therefore, Therefore, solution of the homogeneous equation is Step-4:We know that, is the particular solution of the differential equation.Differentiate both sides we get.Substitute these values in equation (1) we get.Comparing the coefficients we get..Therefore, particular solution of the differential equation is Step-5:We know that, the solution of the differential equation is Therefore, .step-6:We know that , At initial position t = 0, i(0) = 0 and q(0) = 0,then we get., since cos(0) =1 , and sin(0) =0..Step-7:Therefore, the charge of the capacitor q is: .The current in LC circuit i is:

Step 2 of 3

Chapter 5.1, Problem 56E is Solved
Step 3 of 3

Textbook: A First Course in Differential Equations with Modeling Applications
Edition: 10
Author: Dennis G. Zill
ISBN: 9781111827052

This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. This full solution covers the following key subjects: capacitor, Charge, Circuit, current, Find. This expansive textbook survival guide covers 109 chapters, and 4053 solutions. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. The full step-by-step solution to problem: 56E from chapter: 5.1 was answered by , our top Calculus solution expert on 07/17/17, 09:41AM. The answer to “Find the charge on the capacitor and the current in an LC circuit when L = 0.1 h, C = 0.1 f, E(t) = 100 sin ?t V, q(0) = 0 C, and i(0) = 0 A.” is broken down into a number of easy to follow steps, and 37 words. Since the solution to 56E from 5.1 chapter was answered, more than 328 students have viewed the full step-by-step answer.

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Solved: Find the charge on the capacitor and the current