Suppose an RC series circuit has a variable resistor. If the resistance at time t is given by by R = a + bt, where a and b are known positive constants then the charge q(t) on the capacitor satisfies
(a+bt) q' + (1/C)q = V
where V is some constant. Also q(0) = q_0
Find q(t) as an explicit function of t.
Now I have obtained the answer, however my main question is: am I allowed to treat C (capacitance) as a constant in this equation. It doesn't specify in the question, but to my knowledge (unless I am wrong of course) capacitance is a constant value and only depends on material and physical parameters of the capacitor itself (how it is build).
If I can't treat C as a constant then I believe there is no way to evaluate the integral in integrating factor and I'd have to leave it as it is.
Process is simple from there, I rewrite the equation in standart form, find the integrating factor and obtain a formula for q(t), evaluate an integration constant with q(0) = q_0 and obtain the overall solution q(t).
The answer looks quite frightening btw
3. My solution:
attached pdf file
935.7 KB Views: 113