(e) If the initial charge is Q(0) = 0 C, use Euler's method with step size 0.1 to estimate the charge, Q after half a second. (Round your answer to two decimal places.) Q(0.5) - C
(e) If the initial charge is Q(0) = 0 C, use Euler's method with step size 0.1 to estimate the charge, Q after half a second. (Round your answer to two decimal places.) Q(0.5) - C
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![The figure shows a dircuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs, C), so in this case Kirchhoffs Law gives
RI+E().
But I da/dt, so we have
Rd2+ = Q = E(E).
Suppose the resistance is 5 22, the capacitance is 0.1 F, and a battery gives a constant voltage of 60 V.
(a) Draw a direction field for this differential equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1cf29de1-e3f4-4dce-af3b-387ce3b73ca3%2F731427d1-156b-4a3c-bee0-5dc5f5392b5c%2Fseadw4h_processed.png&w=3840&q=75)
Transcribed Image Text:The figure shows a dircuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs, C), so in this case Kirchhoffs Law gives
RI+E().
But I da/dt, so we have
Rd2+ = Q = E(E).
Suppose the resistance is 5 22, the capacitance is 0.1 F, and a battery gives a constant voltage of 60 V.
(a) Draw a direction field for this differential equation.
![(b) What is the limiting value of the charge?
с
(c) Is there an equilibrium solution?
Yes
No
(d) If the initial charge is Q(0) = 0 C, use the direction field to sketch the solution curve.
Q
Q
12
10
8
6
Q
6
5
1
1
1
2
3
3
4
5
6
12
10
8
Q
5
1
2
3
3
4
4
5
5
6
6
t
t
(e) If the initial charge is Q(0) = 0 C, use Euler's method with step size 0.1 to estimate the charge, Q after half a second. (Round your answer to two decimal places.)
Q(0.5) =
с](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1cf29de1-e3f4-4dce-af3b-387ce3b73ca3%2F731427d1-156b-4a3c-bee0-5dc5f5392b5c%2Fh1kyrqq_processed.png&w=3840&q=75)
Transcribed Image Text:(b) What is the limiting value of the charge?
с
(c) Is there an equilibrium solution?
Yes
No
(d) If the initial charge is Q(0) = 0 C, use the direction field to sketch the solution curve.
Q
Q
12
10
8
6
Q
6
5
1
1
1
2
3
3
4
5
6
12
10
8
Q
5
1
2
3
3
4
4
5
5
6
6
t
t
(e) If the initial charge is Q(0) = 0 C, use Euler's method with step size 0.1 to estimate the charge, Q after half a second. (Round your answer to two decimal places.)
Q(0.5) =
с
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