# Capacitance in Parallel and Serial Connections

## Capacitors in parallel and series connections

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### Capacitors in Parallel

For parallel-connected capacitors the equivalent capacitance can be expressed as

C = C_{1}+ C_{2}+ . . + C_{n}(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 / C_{1}+ 1 / C_{2}+ . . + 1 / C_{n}(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 ε _{o} ε_{r }l / ln(r_{2}/r_{1}) (3)*

*where*

*ε _{o} = absolute permittivity, *

*vacuum permittivity*

*(8.85 10*

^{-12}F/m, Farad/m)*ε _{r }= relative permittivity *

*l = length of cylinders*

*r _{2} = radius of inner cylinder*

*r _{1} = radius of outer cylinder*

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