(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

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Chapter1: Units, Trigonometry. And Vectors
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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.
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
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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