limiting value of the charge
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A circuit contains an electromotive force [E(t)], a capacitor with capacitance of C Farads, 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, so Kirchoff's Law gives
R * I + Q/C = E(t)
But I = dQ/dt, so
R * dQ/dt + 1/C * Q = E(t)
If the resistance (R) is 5 ohms, and the capacitance (C) is 0.05 Farads, and a battery gives a constant voltage of 60 V, then
5 * dQ/dt + 1/.05 * Q = 60 , or
dQ/dt + 4Q = 12
So here are my questions:
(a) Using Maple (I am using Maple 15), can you show me the commands to draw a direction field for this differential equation
(b)What is the limiting value of the charge
(c) Is there an equilibrium solution?
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Solution Summary
The potential across the resistor according to Ohm's law is articulated in this solution.
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I have solved the entire problem from scratch just for future reference.
I assume that asking what is the limiting value of the charge you mean is what is the maximum charge the ...
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