# 3.5 Series and parallel circuits

A brief look at series and parallel circuits. Also defines voltage and current divider.

The results shown in other modules ( circuit elements , KVL and KCL , interconnection laws ) with regard to this circuit , and the values of other currents and voltages in this circuit as well, have profound implications.

Resistors connected in such a way that current from one must flow only into another—currents in all resistors connected this way have the samemagnitude—are said to be connected in series . For the two series-connected resistors in the example, the voltage across one resistor equals the ratio of that resistor's value and the sum of resistancestimes the voltage across the series combination . This concept is so pervasive it has a name: voltage divider .

The input-output relationship for this system, found in this particular case by voltage divider, takes the formof a ratio of the output voltage to the input voltage. $\frac{{v}_{\mathrm{out}}}{{v}_{\mathrm{in}}}=\frac{{R}_{2}}{{R}_{1}+{R}_{2}}$ In this way, we express how the components used to build the system affect the input-output relationship. Because thisanalysis was made with ideal circuit elements, we might expect this relation to break down if the input amplitude is too high(Will the circuit survive if the input changes from 1 volt to one million volts?) or if the source's frequency becomes toohigh. In any case, this important way of expressing input-output relationships—as a ratio of output toinput—pervades circuit and system theory.

The current ${i}_{1}$ is the current flowing out of the voltage source. Because it equals ${i}_{2}$ , we have that $\frac{{v}_{\mathrm{in}}}{{i}_{1}}={R}_{1}+{R}_{2}$ :

The series combination of two resistors acts, as far as the voltage source is concerned, as a single resistor having avalue equal to the sum of the two resistances.
This result is the first of several equivalent circuit ideas : In many cases, a complicated circuit when viewed from its terminals (the twoplaces to which you might attach a source) appears to be a single circuit element (at best) or a simple combination ofelements at worst. Thus, the equivalent circuit for a series combination of resistors is a single resistor having aresistance equal to the sum of its component resistances.

Thus, the circuit the voltage source "feels" (through the current drawn from it) is a single resistor having resistance ${R}_{1}+{R}_{2}$ . Note that in making this equivalent circuit, the output voltagecan no longer be defined: The output resistor labeled ${R}_{2}$ no longer appears. Thus, this equivalence is made strictly from the voltage source's viewpoint.

#### Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Answers please
Nikki Reply

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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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