If we have a number of such condensers we can combine them in
"parallel" or in "series." If all the plates on one side are connected
together and also those on the other, the condensers are joined in
parallel. If C1, C2, C3, &c., are the separate capacities, then
[Sigma](C) = C1 + C2 + C3 + &c., is the total capacity in parallel. If
the condensers are so joined that the inner coating of one is
connected to the outer coating of the next, they are said to be in
series. Since then they are all charged with the same quantity of
electricity, and the total over all potential difference V is the sum
of each of the individual potential differences V1, V2, V3, &c., we
have
Q = C1V1 = C2V2 = C3V3 = &c., and V = V1 + V2 + V3 + &c.
The resultant capacity is C = Q/V, and
C = 1/(1/C1 + 1/C2 + 1/C3 + &c.) = 1/[Sigma](1/C) (15).
These rules provide means for calculating the resultant capacity when
any number of condensers are joined up in any way.
If one condenser is charged, and then joined in parallel with another
uncharged condenser, the charge is divided between them in the ratio
of their capacities. For if C1 and C2 are the capacities and Q1 and Q2
are the charges after contact, then Q1/C1 and Q2/C2 are the potential
differences of the coatings and must be equal. Hence Q1/C1 = Q2/C2 or
Q1/Q2 = C1/C2. It is worth noting that if we have a charged sphere we
can perfectly discharge it by introducing it into the interior of
another hollow insulated conductor and making contact. The small
sphere then becomes part of the interior of the other and loses all
charge.
_Measurement of Capacity._--Numerous methods have been devised for the
measurement of the electrical capacity of conductors in those cases in
which it cannot be determined by calculation. Such a measurement may
be an _absolute_ determination or a _relative_ one. The dimensions of
a capacity in electrostatic measure is a length (see UNITS, PHYSICAL).
Thus the capacity of a sphere in electrostatic units (E.S.U.) is the
same as the number denoting its radius in centimetres. The unit of
electrostatic capacity is therefore that of a sphere of 1 cm.
radius.[9] This unit is too small for practical purposes, and hence a
unit of capacity 900,000 greater, called a microfarad, is generally
employed. Thus for instance the capacity in free space of a sphere 2
metres in diameter would be 100/900,000 = 1/9000 of a microfarad. The
electrical capacity of the whole earth considered as a sphere is about
800 microfarads. An absolute measurement of capacity means, therefore,
a determination in E.S. units made directly without reference to any
other condenser. On the other hand there are numerous methods by which
the capacities of condensers may be compared and a relative
measurement made in terms of some standard.
Relative determinations.
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