162 Week 5: Resistance
5.1: Batteries and Voltage Sources
Up to now, we haven’t really consideredhowthe capacitors in the sections above got charged up.
Our model of matter is electrically neutral atoms and molecules, andwhile conductors have lots of
mobile charge we don’t know how tograbthat charge and push it around yet. Or rather, we do –
one way to push it around is to usethe electric field itselfto do the pushing!
This is how one charges things like amber and glass or clouds by rubbingthem. The fields of the
atoms rub together and knock off charges and transfer them preferentially in one direction or the
other. But another way of grabbing things with fields is to exploit theelectrostatic field that holds
atoms and molecules together inchemistry– abattery^47.
Chemical Batteries
It is probably instructive to look at the actual chemical reaction associated with at least onespecific
kind of battery, even though one can make a cell out two different kinds of almostanymetal stuck
into an electrolyte solution (e.g. an acid). So let’s look at the two reactions associated with a
lead-acid battery, the kind you probably have in your car.
A lead-acid battery consists of two plates. The anode (positive pole) is made out of ordinary
lead. The cathode (negative pole) is made of lead coated with lead oxide. Both are immersed in a
solution of water and sulphuric acid. At the anode^48 :
Pb + HSO− 4 →PbSO 4 + H++ 2e−while at the cathode:
PbO 2 + HSO− 4 + 3H++ 2e−→PbSO 4 + 2H 2 O
or overall:
Pb + PbO 2 + 2H 2 SO 4 →2PbSO 4 + 2H 2 O
plus the transfer of two electrons, driven by the chemical energyof the reaction, between the cathode
and the anode.
The electrolyte provides both the (ionized) sulphuric acid required at both ends and a conducting
pathway for the electrons to be transported from the anode to the cathode. Energy is released by
this reaction; the end products aremorestable than the original ones so the reaction isfavored.
However, once a few atoms in the anode have given up their electrons and they’ve been pulled
over to the cathode, the reaction stops! The poles are thencharged upand it costs too much work
to remove any more electrons, more than onegainsin the chemical reaction. The anode is then
charged uppositively(as an electrondonorto the reaction in the battery itself) while the cathode
is charged upnegatively(having received the electrons). The top and bottom plates behavejust like
the plates of a capacitorand maintain an electrical potential difference of around 2 volts (percellin
abatteryof six cells, in a typical twelve volt battery in a car) between them that just balances the
chemical potential of the arrangement.
There is, however, an important difference. If one provides aconducting pathwaybetween the
anode and the cathodeoutsideof the solution, then the negative charge surplus on the cathode can
flowbackover to the anode and participate in another reaction, then another, then another. Charge
continues to be driven in this way until all of the lead and lead oxide is converted into lead sulphate
(^47) Technically, a single device that generates a voltage in this way is called acell– abatteryis composed of several
cells – but we’ll just call anything that generates electricity a battery because nobody speaks of “flashlight cells” when
they go to the store to get a pack of D’s, they say “I’m going to get some batteries for the flashlight”.
(^48) Wikipedia: http://www.wikipedia.org/wiki/Lead-acid battery. There are more complete ways of writing out the
chemical reaction that show more of what is going on with the water in all of this, but this is sufficient. Either way,
you are of course encouraged to visit the link and read more about it.