If you’ve studied capacitors, you’ll have (very probably) come across the decay equation:

where is resistance, is capacitance, is the charge on the capacitor at time and is the initial charge.

#### Where does this come from?

Firstly from the basics of circuits, we know that (yes, I’m using the british convention with regards the symbol for voltage, I understand elsewhere is used instead).

Now when we discharge a capacitor through a circuit, the e.m.f.s are supplied by the capacitor.

Now substitutiting for V in the above equation gives

So we now have an equation for the current in the circuit, but wait, where does this current come from? It’s the capacitor discharging – this current is equal to the rate of discharge of the capacitor, so:

So substituting the above expression for I

Ooh look, a differential equation.

Seperate the variables giving:

where k is some constant.

If we define the initial charge to be – the charge when t = 0

so we now can replace giving:

MY WORK HERE IS DONE

:D

прочитал с большим интересом — очень очень понравилось

Класно! Нашел, наконец толковый блог на просторах интернета) Ура!

Суперский пост! Блог уже в ридере )

Watching mr. Lloyd trying to derive this is hilarious xD