Capacitors - Parallel and Serial Connections
Capacitors in Parallel
Capacitors can be connected in parallel:
The equivalent capacitance for parallel-connected capacitors can be calculated as
C = C 1 + C 2 + . . + C n (1)
where
C = equivalent capacitance for the parallel connected circuit (Farad, F, μF)
C 1..n = capacitance capacitors (Farad, F, μF)
It is common to use µF as the unit for capacitance.
Capacitors in Series
Capacitors can be connected in series:
The equivalent capacitance for series-connected capacitors can be calculated as
1 / C = 1 / C 1 + 1 / C 2 + . . + 1 / C n (2)
For the special case with two capacitors in series - the capacitance can be expressed as
1 / C = ( C 1 + C 2 ) / (C 1 C 2 ) (2b)
- or transformed to
C = C 1 C 2 / (C 1 + C 2 ) (2c)
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)
Capacitors in Series
Three capacitors C 1 = 3 μF , C 2 = 6 μF and C 3 = 12 μF are connected in series as indicated in the figure above. The voltage supply to the circuit is 230 V.
The equivalent circuit capacitance can be calculated with (2)
1 / C = 1 / ( 3 μF ) + 1 / (6 μF ) + 1 / ( 12 μF )
= (4 + 2 + 1) / 12
= 0.58 1/μF
- or transformed
C = 12 / (4 + 2 + 1)
= 1.7 μF
The total charge in the circuit can be calculated with
Q = U C
where
Q = charge (coulomb, C)
U = electric potential (V)
- or with values
Q = (230 V) (1.7 10 -6 F)
= 3.91 10 -4 C
= 391 μC
Since the capacitors are connected in series - the charge is 391 μC on each of them.
The voltage across capacitor 1 can be calculated
U 1 = Q / C 1
= (391 μC) / (3 μF)
= 130 V
The voltage across capacitor 2 can be calculated
U 2 = Q / C 2
= (391 μC) / (6 μF)
= 65 V
The voltage across capacitor 3 can be calculated
U 3 = Q / C 3
= (391 μC) / (12 μF)
= 33 V
Capacitance of Two Coaxial Cylinders
The capacitance of two coaxial cylinders as indicated in the figure can be calculated as
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
Related Topics
• Electrical
Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors.
Related Documents
ASME 31.3 Piping Materials - Allowable Pressure Calculator
Calculate ASME 31.3 allowable pressure
Capacitors
Capacitors and capacitance - charge and unit of charge.
Capacitors - Stored Energy
Potential power and energy stored in capacitors.
Electrical Conductivity - Elements and other Materials
Electric conductance is the ability of a element to conduct an electric current.
Electrical Inductance - Serial and Parallel Connections
Electrical inductance in serial and parallel connected inductors.
Electrical Resistance in Serial and Parallel Networks
Resistors in parallel and serial connections.
Relative Permittivity - the Dielectric Constant
Common materials and their relative permittivity.