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emf x emf s = IR x IR s = R x R s . size 12{ { {"emf" rSub { size 8{x} } } over {"emf" rSub { size 8{s} } } } = { { ital "IR" rSub { size 8{x} } } over { ital "IR" rSub { size 8{s} } } } = { {R rSub { size 8{x} } } over {R rSub { size 8{s} } } } } {}

Solving for emf x size 12{"emf" rSub { size 8{x} } } {} gives

emf x = emf s R x R s . size 12{"emf" rSub { size 8{x} } ="emf" rSub { size 8{s} } { {R rSub { size 8{x} } } over {R rSub { size 8{s} } } } } {}
Two circuits are shown. The first circuit has a cell of e m f script E and internal resistance r connected in series to a resistor R. The second diagram shows the same circuit with the addition of a galvanometer and unknown voltage source connected with a variable contact that can be adjusted up and down the length of the resistor R.
The potentiometer, a null measurement device. (a) A voltage source connected to a long wire resistor passes a constant current I size 12{I} {} through it. (b) An unknown emf (labeled script E x in the figure) is connected as shown, and the point of contact along R size 12{R} {} is adjusted until the galvanometer reads zero. The segment of wire has a resistance R x size 12{R rSub { size 8{x} } } {} and script E x = IR x size 12{E rSub { size 8{x} } = ital "IR" rSub { size 8{x} } } {} , where I size 12{I} {} is unaffected by the connection since no current flows through the galvanometer. The unknown emf is thus proportional to the resistance of the wire segment.

Because a long uniform wire is used for R size 12{R} {} , the ratio of resistances R x / R s size 12{R rSub { size 8{x} } /R rSub { size 8{s} } } {} is the same as the ratio of the lengths of wire that zero the galvanometer for each emf. The three quantities on the right-hand side of the equation are now known or measured, and emf x size 12{"emf" rSub { size 8{x} } } {} can be calculated. The uncertainty in this calculation can be considerably smaller than when using a voltmeter directly, but it is not zero. There is always some uncertainty in the ratio of resistances R x / R s size 12{R rSub { size 8{x} } /R rSub { size 8{s} } } {} and in the standard emf s size 12{"emf" rSub { size 8{s} } } {} . Furthermore, it is not possible to tell when the galvanometer reads exactly zero, which introduces error into both R x size 12{R rSub { size 8{x} } } {} and R s size 12{R rSub { size 8{s} } } {} , and may also affect the current I size 12{I} {} .

Resistance measurements and the wheatstone bridge

There is a variety of so-called ohmmeters that purport to measure resistance. What the most common ohmmeters actually do is to apply a voltage to a resistance, measure the current, and calculate the resistance using Ohm’s law. Their readout is this calculated resistance. Two configurations for ohmmeters using standard voltmeters and ammeters are shown in [link] . Such configurations are limited in accuracy, because the meters alter both the voltage applied to the resistor and the current that flows through it.

The diagram shows two circuits. The first one has a cell of e m f script E and internal resistance r connected in series to an ammeter A and a resistor R. The second circuit is the same as the first, but in addition there is a voltmeter connected across the voltage source E.
Two methods for measuring resistance with standard meters. (a) Assuming a known voltage for the source, an ammeter measures current, and resistance is calculated as R = V I size 12{R= { {V} over {I} } } {} . (b) Since the terminal voltage V size 12{V} {} varies with current, it is better to measure it. V size 12{V} {} is most accurately known when I size 12{I} {} is small, but I size 12{I} {} itself is most accurately known when it is large.

The Wheatstone bridge    is a null measurement device for calculating resistance by balancing potential drops in a circuit. (See [link] .) The device is called a bridge because the galvanometer forms a bridge between two branches. A variety of bridge devices are used to make null measurements in circuits.

Resistors R 1 size 12{R rSub { size 8{1} } } {} and R 2 size 12{R rSub { size 8{2} } } {} are precisely known, while the arrow through R 3 size 12{R rSub { size 8{3} } } {} indicates that it is a variable resistance. The value of R 3 size 12{R rSub { size 8{3} } } {} can be precisely read. With the unknown resistance R x size 12{R rSub { size 8{x} } } {} in the circuit, R 3 size 12{R rSub { size 8{3} } } {} is adjusted until the galvanometer reads zero. The potential difference between points b and d is then zero, meaning that b and d are at the same potential. With no current running through the galvanometer, it has no effect on the rest of the circuit. So the branches abc and adc are in parallel, and each branch has the full voltage of the source. That is, the IR size 12{ ital "IR"} {} drops along abc and adc are the same. Since b and d are at the same potential, the IR size 12{ ital "IR"} {} drop along ad must equal the IR size 12{ ital "IR"} {} drop along ab. Thus,

Questions & Answers

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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
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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Source:  OpenStax, College physics -- hlca 1104. OpenStax CNX. May 18, 2013 Download for free at http://legacy.cnx.org/content/col11525/1.1
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