The Series and parallel circuits reference article from the English Wikipedia on 24-Jul-2004
(provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Series and parallel circuits

Connect with a children's charity on your social network
Image:Series and parallel circuits.png
Circuits
Left: Series  | Right: Parallel
Arrows indicate direction of current flow.
The red bars represent the voltage.

In electrical circuits series and parallel are two basic ways of wiring components. The naming comes after the method of attaching components, i.e. one after the other, or next to each other. As a demonstration, consider a very simple circuit consisting of two lightbulbs and one 9V battery. If a wire joins the battery to one bulb, to the next bulb, then back to the battery, in one continuous loop, the bulbs are said to be in series. If, on the other hand, each bulb is wired separately to the battery in two loops, the bulbs are said to be in parallel.

The measurable quantities used here are R, resistance, measured in ohms (Ω), I, current, measured in amperes (A) (coulombs per second), and V, voltage, measured in volts (V) (joules per coulomb).

Table of contents
1 Series circuits
2 Parallel circuits

Series circuits

Series circuits are sometimes called cascade-coupled or daisy chain-coupled.

The same current has to pass through all the components in the series. An ammeter placed anywhere in the circuit would measure the same amount.

A diagram of several resistors, connected end to end, with the same amount of current going through each

Rtotal = R1 + R2 + ... + Rn

for components in series, having resistances R1, R2, etc.

I = V/Rtotal

V=IRi
Where I is the current, as calculated above.

Note that the components divide the voltage according to their resistances, so, in the case of two resistors, V1/V2 = R1/R2

Inductors follow the same law, in that the total inductance of inductors in series is equal to the sum of their individual inductances:

A diagram of several inductors, connected end to end, with the same amount of current going through each

Capacitors follow a different law. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances:

A diagram of several capacitors, connected end to end, with the same amount of current going through each

Parallel circuits

The
voltage is the same across all the components in parallel.

A diagram of several resistors, side by side, both leads of each connected to the same wires

1 / Rtotal = 1 / R1 + 1 / R2 + ... + 1 / Rn

for components in parallel, having resistances R1, R2, etc.

The above rule can be calculated by using Ohm's law for the whole circuit
Rtotal =V/Itotal
and substituting for Itotal

Ii = V/Ri

Note, that the components divide the current according to their reciprocal resistances, so, in the case of two resistors, I1/I2 = R2/R1

Inductors follow the same law, in that the total inductance of inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:

A diagram of several inductors, side by side, both leads of each connected to the same wires

Capacitors follow a different law. The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances:

A diagram of several capacitors, side by side, both leads of each connected to the same wires

Notation

The parallel property can be represented in equations by two vertical lines "||" (as in geometry) to simplify equations. For two resistors,