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# limiting value of the charge

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?

#### Solution Preview

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 ...

#### Solution Summary

The potential across the resistor according to Ohm's law is articulated in this solution.

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