Capacitors in Series & Parallel (CIE A Level Physics)

Revision Note

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Author

Ann H

Last updated

27 October 2024

Capacitors in series & parallel

Like resistors, capacitors can be combined in series and parallel
- Often, circuits may contain combinations of capacitors in both series and parallel arrangements

In a series arrangement:
- the reciprocal of the combined capacitance is equal to the sum of the reciprocals of the individual capacitances
- the combined capacitance of two identical capacitors is equal to half of the value of each one
- the combined capacitance is always less than the value of the smallest individual capacitance

In a parallel arrangement:
- the combined capacitance is equal to the sum of all the individual capacitances
- the combined capacitance of two identical capacitors is equal to twice the value of each one
- the combined capacitance is always greater than the value of the any individual capacitance

Worked example

Three capacitors with capacitance of 23 μF, 35 μF and 40 μF are connected as shown below.

WE Capacitors in Series & Parallel question image, downloadable AS & A Level Physics revision notes

Calculate the total capacitance between points A and B.

Answer:

Step 1: Calculate the combined capacitance of the two capacitors in parallel

To calculate capacitance in parallel:

C_total = C₁+ C₂ + C₃ …

C_parallel= 23 + 35 = 58 μF

Step 2: Connect this combined capacitance with the final capacitor in series

To calculate capacitance in series:

$\frac{1}{C_{total}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}} . . . . .$

$\frac{1}{C_{total}} = \frac{1}{58} + \frac{1}{40} = \frac{49}{1160}$

Step 3: Rearrange for the total capacitance

$C_{total} = \frac{1160}{49} = 23.673 . . . = 24 μF (2 s . f .)$

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Author: Ann H

Expertise: Physics

Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students no matter their schooling or background.