Question: The figure shows a circuit containing an
The figure shows a circuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (Ω). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs, C), so in this case Kirchhoff’s Law gives
Suppose the resistance is 5Ω, the capacitance is 0.00F, 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?
(c). Is there an equilibrium solution?
(d). If the initial charge is Q (0) = 0C, use the direction field to sketch the solution curve.
(e). If the initial charge is Q (0) = 0 C, use Euler’s method with step size 0.1 to estimate the charge after half a second.
Transcribed Image Text:
RI + = E() But I = dQ/dt, so we have ÕP R dt = E(t) C E
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