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A brief look at series and parallel circuits. Also defines voltage and current divider.
The circuit shown is perhaps the simplest circuit that performs a signal processing function. The input is providedby the voltage source v in and the output is the voltage v out across the resistor labelled R 2 .

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. v out v in 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 v 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.

The resistor (on the right) is equivalent to the two resistors (on the left) and has a resistance equal to the sum of theresistances of the other two resistors.

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

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.
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
I only see partial conversation and what's the question here!
Crow Reply
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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