Tutorial 2 - Deriving the Equations for Capacitor Circuits

Series

Consider this circuit consisting of two capacitors in parallel. They have values C1 and C2 and are connected to a battery of voltage V.

The basic equation is:

Q = CV

So the charge across each capacitor is:

Q = C1V and Q = C2V

So, from the summation of charge, we can write:

Qtot = Q1 + Q2

And then substitute:

CtotV = C1V + C2V

The voltage terms, V, cancel out to leave us with:

Ctot = C1 + C2

 

Series Capacitors

Here is a circuit consisting of two capacitors in series. They have values C1 and C2 and are connected to a battery of voltage V.

In any series circuit

 

The voltages adding up is Kirchhoff II and we can therefore write:

Vtot = V1 + V2

Now we can write the charge equation in terms of V:

We can also write the different voltages as:

So we can rewrite the Kirchhoff II equation as:

Since the charge is the same, the Q terms cancel to give:

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