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Capacitors in Parallel and Series
Capacitors and parallel and series capacitance
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Capacitors in Parallel
For parallel-connected capacitors the equivalent capacitance can be expressed as
C = C1 + C2 + . . + Cn (1)
where
C = capacitance (Farad, F, μF)
It is common to use µF.
Capacitors in Series
For series-connected capacitors the equivalent capacitance can be expressed as
1/C = 1/C1 + 1/C2 + . . + 1/Cn (2)
Example - Capacitors Connected in Parallel and in Series
The equivalent capacitance of two capacitors with capacitance 10 μF and 20 μF can be calculated as
in parallel
C = (10 μF) + (20 μF)
= 30 (μF)
in series
1/C = 1/(10 μF) + 1/(20 μF)
= 0.15 (1/μF)
or
C = 1 / 0.15 (1/μF)
= 6.7 (μF)
Capacitance of Two Coaxial Cylinders
C = 2 π εo εr l / ln(r2/r1) (3)
where
εo = absolute permittivity, vacuum permittivity (8.85 10-12 F/m, Farad/m)
l = length of cylinders
r2 = radius of inner cylinder
r1 = radius of outer cylinder
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