   Chapter 17, Problem 19RE

Chapter
Section
Textbook Problem

A series circuit contains a resistor with R = 40 Ω, an inductor with L = 2 H, a capacitor with C = 0.0025 F, and a 12-V battery. The initial charge is Q = 0.01 C and the initial current is 0. Find the charge at time t.

To determine

To find: The charge at time t.

Explanation

Given data:

The values of, the resistor R is 40Ω , an inductor L is 2 H, a capacitor C is 0.0025 F, and battery E is 12 V.

Write the expression for the differential equation,

LQ+RQ+1CQ=E (1)

Substitute 2 H for L, 40Ω for R, 0.0025 F for C and 12 V for E in equation (1),

2Q+40Q+10.0025Q=12

2Q+40Q+400Q=12 (2)

Consider the auxiliary equation,

2r2+40r+400=0

r2+20r+200=0 (3)

Roots of equation (3) are,

r=20±(20)24(1)(200)2(1){r=b±b24ac2afortheequationofar2+br+c=0}=20±i202=10±i10

Write the expression for the complementary solution of two complex roots r=α±iβ ,

Qc(t)=eαt(c1cosβt+c2sinβt) (4)

Substitute 10 for α and 10 for β in equation (4),

Qc(t)=e10t(c1cos10t+c2sin10t) (5)

The Right hand side (RHS) of a differential equation contains only a numerical value, and then the particular solution for this case can be expressed as follows

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

(a) By comparing areas, show that ln 2 1 ln 3. (b) Deduce that 2 e 3.

Single Variable Calculus: Early Transcendentals, Volume I

(t+6)(60)(60t+180)(t+6)2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Simplify: 99

Elementary Technical Mathematics 