1st order linear ODE example: RC circuit. Solve for the general expression for I

Question

1st order linear ODE example: RC circuit. Solve for the general expression for I(t) without assuming any specific forcing function Vin(t) or initial conditions. Note that capacitors are storage elements and the voltage drop across a capacitor is VC(t) = 1 / C I(t)dt. Hint: You will need to take the time derivative of Kirchhoff's Voltage Law. Since the forcing function has not been defined, it will need to remain inside the integral term which will appear in your solution. Your answer may have an undefined constant term.

Explanation / Answer

Now the question already tells us we have to use I(t). So we know without thinking anything that

I(t) = Something, Right?

*Hint: Using the kirchhoff's law*

We can derive the function that Vc(t)= 1/Cƒ I (t) dt.

We can combine this with Kirchhoff's law

Which will then look like this expression :

Therefore = I(t)= d/dt[Vc] * c

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