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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

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..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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.
yes that's correct
I think
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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
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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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