Electronics/Simplifying Capacitor/Inductor Networks

Introduction

Capacitors and inductors follow similar laws as resistors when it comes to simplification.

Simplifying Capacitor Configurations

Capacitors in Parallel

Capacitors in parallel are the same as increasing the total surface area of the capacitors to create a larger capacitor with more capacitance. In a capacitor network in parallel, all capacitors have the same voltage over them.

File:Electronics Capacitorsparallel.png

In a parallel configuration, the capacitance of the capacitors in parallel is the sum of the capacitance of all the capacitors.

${\displaystyle C_{eq}=C_{1}+C_{2}+\cdots +C_{n}\,\!}$

Capacitors in Series

Capacitors in series are the same as increasing the distance between two capacitor plates. As well, it should be noted that placing two 100V capacitors in series results in the same as having one capacitor with the total maximum voltage of 200V. This, however, is not recommended to be done in practice. Especially with capacitors of different values. In a capacitor network in series, all capacitors can have the a different voltage over them.

In a series configuration, the capacitance of all the capacitors combined is the sum of the reciprocals of the capacitance of all the capacitors.

${\displaystyle {\frac {1}{C_{eq}}}={\frac {1}{C_{1}}}+{\frac {1}{C_{2}}}+\cdots +{\frac {1}{C_{n}}}}$

Simplifying Inductor Configurations

An inductor works by opposing current change

Inductors in Parallel

Each inductor has a decreased amount of current flowing through it.
Take two inductors of the same strength that are in parallel. This divides the current so half the current is flowing through each inductor.

${\displaystyle {\frac {1}{L_{eq}}}={\frac {1}{L_{1}}}+{\frac {1}{L_{2}}}+\cdots +{\frac {1}{L_{n}}}}$

Inductors in Series

Inductors in series are just like resistors in series. Simply add them up.