Circuit with resistor, switch and capacitor

[gneill]

Yup. Looks good.

 

[johann1301h]

This is great!

But you mentioned in post #13

That is the "starting from the basics" approach, yes.

The thing is this, in the next task I'm asked to verify the result using a numerical method; ie. using a differential equation! (forward Euler for instance)

But I/we have solved it, by simply assuming the "form" of the function; I guess I am puzzled by the "starting from the basics" approach" you mentioned...

How does one go about finding the differential equation?

 

[gneill]

How does one go about finding the differential equation?

One writes the circuit equations using the differential or integral forms for the capacitor voltage or current, then solve the resulting differential equation. So for example, for the simple case of a charged capacitor discharging through a resistor, writing KCL:

$C \frac{dV}{dt} +\frac{V}{R} = 0$

$\frac{dV}{dt} = -\frac{V}{R C}$

$\frac{dV}{V} = -\frac{dt}{R C}$

and so on