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** Previous:** Example 6.2: Dielectric filled

*Question:*
A and a capacitor are connected in parallel, and this pair of
capacitors is then connected in series with a capacitor, as
shown in the diagram.
What is the equivalent capacitance of the whole combination?
What is the charge on the capacitor if
the whole combination is connected across the terminals of
a V battery? Likewise, what are the charges on the
and capacitors?

*Answer:* The equivalent capacitance of the and
capacitors connected in parallel is
.
When a capacitor is combined in series with a
capacitor,
the equivalent capacitance of the whole combination is given by

and so

The charge delivered by the V battery is

This is the charge on the capacitor, since one of the terminals
of the battery is connected directly to one of the plates of this capacitor.
The voltage drop across the capacitor is

Thus, the voltage drop across the and combination
must be
. The charge stored on the
is given by

Likewise, the charge stored on the capacitor is

Note that the total charge stored on the and combination
is
, which is the same as the charge
stored on the capacitor. This makes sense because the and combination
and the capacitor are connected in series.

** Next:** Example 6.4: Energy stored
** Up:** Capacitance
** Previous:** Example 6.2: Dielectric filled
Richard Fitzpatrick
2007-07-14