**Tutorial 2 - Deriving the Equations for Capacitor Circuits**

Consider this circuit consisting of two
capacitors in **parallel**. They have values *C*_{1} and *C*_{2
}and are connected to a battery of voltage *V*.

- Like all parallel circuits the voltage
across the capacitors is the
**same**. - The total charge is the
**sum**of the charges on the capacitors. It’s like the currents in parallel resistors adding up.

The basic equation is:

*Q = CV*

So the charge across each capacitor is:

*Q = C*_{1}*V* and
*Q = C*_{2}*V*

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

*Q*_{tot}* = Q*_{1}*
+ Q*_{2}

And then substitute:

*C*_{tot}*V = C*_{1}*V
+ C*_{2}*V*

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

*C*_{tot}* = C*_{1}*
+ C*_{2}

Here is a circuit consisting of two
capacitors in **series**. They have values *C*_{1 }and *C*_{2
}and are connected to a battery of voltage *V*.

In any series circuit

- The voltages
**add up to the battery voltage**; - The current (charge) is the
**same all the way round**.

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

*V*_{tot} = *V*_{1}*
+ V*_{2}

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: