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  • Draw a circuit with resistors in parallel and in series.
  • Calculate the voltage drop of a current across a resistor using Ohm’s law.
  • Contrast the way total resistance is calculated for resistors in series and in parallel.
  • Explain why total resistance of a parallel circuit is less than the smallest resistance of any of the resistors in that circuit.
  • Calculate total resistance of a circuit that contains a mixture of resistors connected in series and in parallel.

Most circuits have more than one component, called a resistor    that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance    . The simplest combinations of resistors are the series and parallel connections illustrated in [link] . The total resistance of a combination of resistors depends on both their individual values and how they are connected.

In part a of the figure, resistors labeled R sub 1, R sub 2, R sub 3, and R sub 4 are connected in series along one path of a circuit. In part b of the figure, the same resistors are connected along parallel paths of a circuit.
(a) A series connection of resistors. (b) A parallel connection of resistors.

Resistors in series

When are resistors in series    ? Resistors are in series whenever the flow of charge, called the current    , must flow through devices sequentially. For example, if current flows through a person holding a screwdriver and into the Earth, then R 1 size 12{R rSub { size 8{1} } } {} in [link] (a) could be the resistance of the screwdriver’s shaft, R 2 size 12{R rSub { size 8{2} } } {} the resistance of its handle, R 3 size 12{R rSub { size 8{3} } } {} the person’s body resistance, and R 4 size 12{R rSub { size 8{4} } } {} the resistance of her shoes.

[link] shows resistors in series connected to a voltage    source. It seems reasonable that the total resistance is the sum of the individual resistances, considering that the current has to pass through each resistor in sequence. (This fact would be an advantage to a person wishing to avoid an electrical shock, who could reduce the current by wearing high-resistance rubber-soled shoes. It could be a disadvantage if one of the resistances were a faulty high-resistance cord to an appliance that would reduce the operating current.)

Two electrical circuits are compared. The first one has three resistors, R sub one, R sub two, and R sub three, connected in series with a voltage source V to form a closed circuit. The first circuit is equivalent to the second circuit, which has a single resistor R sub s connected to a voltage source V. Both circuits carry a current I, which starts from the positive end of the voltage source and moves in a clockwise direction around the circuit.
Three resistors connected in series to a battery (left) and the equivalent single or series resistance (right).

To verify that resistances in series do indeed add, let us consider the loss of electrical power, called a voltage drop    , in each resistor in [link] .

According to Ohm’s law    , the voltage drop, V size 12{V} {} , across a resistor when a current flows through it is calculated using the equation V = IR size 12{V= ital "IR"} {} , where I size 12{I} {} equals the current in amps (A) and R size 12{R} {} is the resistance in ohms Ω size 12{ left ( %OMEGA right )} {} . Another way to think of this is that V size 12{V} {} is the voltage necessary to make a current I size 12{I} {} flow through a resistance R size 12{R} {} .

So the voltage drop across R 1 size 12{R rSub { size 8{1} } } {} is V 1 = IR 1 size 12{V rSub { size 8{1} } = ital "IR" rSub { size 8{1} } } {} , that across R 2 size 12{R rSub { size 8{2} } } {} is V 2 = IR 2 size 12{V rSub { size 8{2} } = ital "IR" rSub { size 8{2} } } {} , and that across R 3 size 12{R rSub { size 8{3} } } {} is V 3 = IR 3 size 12{V rSub { size 8{3} } = ital "IR" rSub { size 8{3} } } {} . The sum of these voltages equals the voltage output of the source; that is,

V = V 1 + V 2 + V 3 . size 12{V=V rSub { size 8{1} } +V rSub { size 8{2} } +V rSub { size 8{3} } } {}

This equation is based on the conservation of energy and conservation of charge. Electrical potential energy can be described by the equation PE = qV size 12{ ital "PE"= ital "qV"} {} , where q size 12{q} {} is the electric charge and V size 12{V} {} is the voltage. Thus the energy supplied by the source is qV size 12{ ital "qV"} {} , while that dissipated by the resistors is

qV 1 + qV 2 + qV 3 . size 12{ ital "qV" rSub { size 8{1} } + ital "qV" rSub { size 8{2} } + ital "qV" rSub { size 8{3} } } {}

Connections: conservation laws

The derivations of the expressions for series and parallel resistance are based on the laws of conservation of energy and conservation of charge, which state that total charge and total energy are constant in any process. These two laws are directly involved in all electrical phenomena and will be invoked repeatedly to explain both specific effects and the general behavior of electricity.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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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
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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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