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)
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?
Here it is.
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 capacitor can hold ...
The potential across the resistor according to Ohm's law is articulated in this solution.