Series and Parallel Capacitors

At the end of this module, you are expected to:
A. explain the difference of capacitors connected in
series and parallel in terms of capacitance, potential
difference, and charge.
B. calculate the equivalent capacitance of a network
of capacitors connected in series/parallel
C. give the importance of capacitors in electronics.

As for any capacitor, the capacitance of the
combination is related to both charge and voltage:
𝐶= 𝑄/𝑉
When this series combination is connected to a
battery with voltage V, each of the capacitors
acquires an identical charge Q.

Charge on this equivalent capacitor is the same as
the charge on any capacitor in a series combination:
That is, all capacitors of a series combination have
the same charge.
𝑄𝑇= 𝑄1= 𝑄2= 𝑄3
any number of capacitors connected in series is
equivalent to one capacitor whose capacitance
(called the equivalent capacitance) is smaller than
the smallest of the capacitances in the series
combination.

We can find an expression for the total (equivalent)
capacitance by considering the voltages across the
individual capacitors. The potentials across
capacitors 1, 2, and 3 are, respectively,
These potentials must sum up to the voltage of the
battery, giving the following potential balance:
𝑉𝑇 =𝑉1+ 𝑉2+ 𝑉3+⋯

An expression containing the equivalent
capacitance, CT, of three capacitors connected in
series:

Sample Problem
Four capacitors with the capacitance of 4 μF, 3 μF,
6 μF, and 12 μF respectively are connected in series
with a battery of 12.0 V. Determine the following:
(a) Equivalent capacitance
(b) Total charge
(c) Individual voltage

The Parallel Combination of Capacitors
Capacitors that are connected in parallel have the
same voltage V across their plates.
A parallel combination of three capacitors, with one
plate of each capacitor connected to one side of the
circuit and the other plate connected to the other
side.

To find the equivalent capacitance CT of the parallel
network, we note that the total charge Q stored by
the network is the sum of all the individual charges:
𝑄𝑇= 𝑄1+ 𝑄2+ 𝑄3+⋯

the equivalent capacitance of the parallel network of
three capacitors: 𝐶𝑇= 𝐶1+ 𝐶2+ 𝐶3+⋯

Sample Problem
Four capacitors with the capacitance of 4 μF, 3 μF,
6 μF, and 12 μF respectively are connected in
parallel with a battery of 12.0 V. Determine the
following:
(a) Equivalent capacitance
(b) Total charge
(c) Individual charges

Energy stored in a simple capacitor
The energy stored in a capacitor is potential energy.
It can be extracted from the capacitor and
transforms into other forms of energy, or can be
used to do mechanical work.

Sample Problem
A heart defibrillator delivers 500 J of energy by
discharging a capacitor initially at 20,000 V. What is
its capacitance?