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[[Image:Tuning fork on resonator.jpg|thumb|right|250px|Tuning fork on resonance box, by Max Kohl, Chemnitz, Germany]]
[[Image:Wheatstonebridge.svg|right|thumb|300px|alt=A Wheatstone bridge has four resistors forming the sides of a diamond shape. A battery is connected across one pair of opposite corners, and a galvanometer across the other pair. |Wheatstone bridge [[circuit diagram]].]]
A '''Wheatstone bridge''' is an electrical circuit used to measure an unknown [[electrical resistance]] by balancing two legs of a [[bridge circuit]], one leg of which includes the unknown component. Its operation is similar to the original [[Potentiometer (measuring instrument)|potentiometer]]. It was invented by [[Samuel Hunter Christie]] in 1833 and improved and popularized by Sir [[Charles Wheatstone]] in 1843.  One of the Wheatstone bridge's initial uses was for the purpose of soils analysis and comparison.<ref>"The Genesis of the Wheatstone Bridge" by Stig Ekelof discusses [[Samuel Hunter Christie|Christie's]] and [[Charles Wheatstone|Wheatstone]]'s contributions, and why the bridge carries Wheatstone's name. Published in "Engineering Science and Education Journal", volume 10, no 1, February 2001, pages 37–40.</ref>


A '''tuning fork''' is an [[Musical acoustics|acoustic]] [[resonator]] in the form of a two-pronged [[fork]] with the prongs ([[Tine (structural)|tines]]) formed from a U-shaped bar of [[Elastic deformation|elastic]] metal (usually [[steel]]).  It [[resonance|resonates]] at a specific constant [[pitch (music)|pitch]] when set vibrating by striking it against a surface or with an object, and emits a pure musical tone after waiting a moment to allow some high [[overtones]] to die out. The pitch that a particular tuning fork generates depends on the length and mass of the two prongs. It is frequently used as a standard of pitch to tune musical instruments.
== Operation ==
In the figure, <math>\scriptstyle R_x</math> is the unknown resistance to be measured; <math>\scriptstyle R_1</math>, <math>\scriptstyle R_2</math> and <math>\scriptstyle R_3</math> are resistors of known resistance and the resistance of <math>\scriptstyle R_2</math> is adjustable. If the ratio of the two resistances in the known leg <math>\scriptstyle (R_2 / R_1)</math> is equal to the ratio of the two in the unknown leg <math>\scriptstyle (R_x / R_3)</math>, then the [[voltage]] between the two midpoints ('''B''' and '''D''') will be zero and no [[Current (electricity)|current]] will flow through the [[galvanometer]] <math>\scriptstyle V_g</math>. If the bridge is unbalanced, the direction of the current indicates whether <math>\scriptstyle R_2</math> is too high or too low. <math>\scriptstyle R_2</math> is varied until there is no current through the galvanometer, which then reads zero.  


The tuning fork was invented in 1711 by British musician [[John Shore (trumpeter)|John Shore]], Sergeant [[Trumpet]]er and [[Lute]]nist to the court.<ref>{{cite journal |pmid=9172630 |year=1997 |last1=Feldmann |first1=H |title=History of the tuning fork. I: Invention of the tuning fork, its course in music and natural sciences. Pictures from the history of otorhinolaryngology, presented by instruments from the collection of the Ingolstadt German Medical History Museum |volume=76 |issue=2 |pages=116–22 |doi=10.1055/s-2007-997398 |journal=Laryngo- rhino- otologie}}</ref>
Detecting zero current with a [[galvanometer]] can be done to extremely high accuracy. Therefore, if <math>\scriptstyle R_1</math>, <math>\scriptstyle R_2</math> and <math>\scriptstyle R_3</math> are known to high precision, then <math>\scriptstyle R_x</math> can be measured to high precision. Very small changes in <math>\scriptstyle R_x</math> disrupt the balance and are readily detected.


==Description==
At the point of balance, the ratio of
[[Image:TuningFork659Hz.jpg|thumb|Tuning fork by John Walker stamped with note (E) and frequency in hertz (659)]]
:<math>\begin{align}
[[Image:Tuning fork on carbon black.jpg|thumb|A needle on a tuning fork carves figures on carbon black.]]
  \frac{R_2}{R_1} &= \frac{R_x}{R_3} \\
  \Rightarrow R_x &= \frac{R_2}{R_1} \cdot R_3
\end{align}</math>


The main reason for using the fork shape is that, unlike many other types of resonators, it produces a very [[pure tone]], with most of the vibrational energy at the [[fundamental frequency]], and little at the [[overtone]]s ([[harmonic]]s).  The reason for this is that the frequency of the first overtone is about 5<sup>2</sup>/2<sup>2</sup> = 25/4 = 6¼ times the fundamental (about 2½ octaves above it).<ref>{{cite book
Alternatively, if <math>\scriptstyle R_1</math>, <math>\scriptstyle R_2</math>, and <math>\scriptstyle R_3</math> are known, but <math>\scriptstyle R_2</math> is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of <math>\scriptstyle R_x</math>, using [[Kirchhoff's circuit laws]] (also known as Kirchhoff's rules). This setup is frequently used in [[strain gauge]] and [[resistance thermometer]] measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.
  | last = Tyndall
  | first = John
  | authorlink =
  | coauthors =
  | title = Sound
  | publisher = D. Appleton & Co.
  | year = 1915
  | location = New York
  | page = 156
  | url = http://books.google.com/books?id=hCgZAAAAYAAJ&pg=PA156
  | doi =
  | id =
  | isbn = }}</ref> By comparison, the first overtone of a vibrating string or metal bar is only one octave above the fundamental.  So when the fork is struck, little of the energy goes into the overtone modes; they also die out correspondingly faster, leaving the fundamental.  It is easier to tune other instruments with this pure tone.


Another reason for using the fork shape is that, when it vibrates in its principal mode, the handle vibrates up and down as the prongs move apart and together.  There is a [[node (physics)|node]] (point of no vibration) at the base of each prong.  The handle motion is small, allowing the fork to be held by the handle without damping the vibration, but it allows the handle to transmit the vibration to a [[resonator]], which amplifies the sound of the fork.<ref>The Science of Sound,  3rd ed., Rossing, Moore, and Wheeler</ref>  The fork is usually struck, and then the handle is pressed against a wooden box resonator, or a table top.  Without the resonator the sound is very faint. The reason for this is that the sound waves produced by each fork prong are 180° out of [[phase (waves)|phase]] with the other, so at a distance from the fork they [[Interference (wave motion)|interfere]] and largely cancel each other out.  If a sound absorbing sheet is slid in between the prongs of a vibrating fork, reducing the waves reaching the ear from one prong, the volume heard will actually increase, due to a reduction of this cancellation.
==Derivation==
First, [[Kirchoff's first law|Kirchhoff's first rule]] is used to find the currents in junctions '''B''' and '''D''':


Although commercial tuning forks are normally tuned to the correct pitch at the factory, they can be retuned by filing material off the prongs.  Filing the ends of the prongs raises the pitch, while filing the inside of the base of the prongs lowers it.
:<math>\begin{align}
  I_3 - I_x + I_G &= 0 \\
  I_1 - I_2 - I_G &= 0
\end{align}</math>


Currently, the most common tuning fork sounds the note of [[A440 (pitch standard)|A = 440 Hz]], because this is the standard [[concert pitch]], which is used as tuning note by some orchestras, it being the pitch of the violin's second string, the first string of the viola, and an octave above the first string of the cello, all played open.  Tuning forks used by orchestras between 1750 and 1820 mostly had a frequency of A = 423.5&nbsp;Hz, although there were many forks and many slightly different pitches.<ref>The Physics of Musical Instruments [http://www.amazon.com/dp/0387983740/ amazon.com]{{Page needed|date=January 2012}}</ref>  Standard tuning forks are available that vibrate at all the musical pitches within the central octave of the piano, and other pitches.  Well-known manufacturers of tuning forks include Ragg and John Walker, both of [[Sheffield]], [[England]].
Then, [[Kirchhoff's circuit laws#Kirchhoff's voltage law (KVL)|Kirchhoff's second rule]] is used for finding the voltage in the loops '''ABD''' and '''BCD''':


The pitch of a tuning fork can vary slightly with weathering and temperature. A change in frequency of one vibration in 21,000 for each °F (86 ppm per °C) change is typical for a steel tuning fork, flattened by heat and sharpened by cold.<ref>[http://books.google.com/books?id=xqU9AQAAIAAJ&pg=PA297#v=onepage&q&f=false Journal of the Society of Arts, Vol. 28], p. 297</ref> The [[Standard conditions for temperature and pressure|standard temperature]] is now 68 °F (20 °C) but 59 °F (15 °C) is an older standard. The pitches of a musical instrument such as an organ are also subject to variation with temperature change.
:<math>\begin{align}
  (I_3 \cdot R_3) - (I_G \cdot R_G) - (I_1 \cdot R_1) &= 0 \\
  (I_x \cdot R_x) - (I_2 \cdot R_2) + (I_G \cdot R_G) &= 0
\end{align}</math>


==Calculation of frequency==
When the bridge is balanced, then {{math|''I''<sub>''G''</sub> {{=}} 0}}, so the second set of equations can be rewritten as:
The frequency of a tuning fork depends on its dimensions and the material from which it is made:<ref>{{cite journal |doi=10.1006/jsvi.1999.2257 |title=Dynamics of Transversely Vibrating Beams Using Four Engineering Theories |year=1999 |last1=Han |first1=Seon M. |last2=Benaroya |first2=Haym |last3=Wei |first3=Timothy |journal=Journal of Sound and Vibration |volume=225 |issue=5 |pages=935}}</ref>
:<math>\begin{align}
  I_3 \cdot R_3 &= I_1 \cdot R_1 \\
  I_x \cdot R_x &= I_2 \cdot R_2
\end{align}</math>


:<math>f  = \frac{1.875^2}{2\pi l^2} \sqrt\frac{EI}{\rho A}</math>
Then, the equations are divided and rearranged, giving:
:<math>R_x = {{R_2 \cdot I_2 \cdot I_3 \cdot R_3}\over{R_1 \cdot I_1 \cdot I_x}}</math>


Where:
From the first rule, {{math|''I''<sub>''3''</sub> {{=}} ''I''<sub>''x''</sub>}} and {{math|''I''<sub>''1''</sub> {{=}} ''I''<sub>''2''</sub>}}.  The desired value of {{math|''R''<sub>''x''</sub>}} is now known to be given as:
* ''f'' is the [[frequency]] the fork vibrates at in [[Hertz]].
:<math>R_x = {{R_3 \cdot R_2}\over{R_1}}</math>
* 1.875 the smallest positive solution of cos(''x'')cosh(''x'') = -1.<ref>{{cite web
  | url=http://emweb.unl.edu/Mechanics-Pages/Scott-Whitney/325hweb/Beams.htm
  | title=Vibrations of Cantilever Beams: Deflection, Frequency, and Research Uses
  | last=Whitney
  | first=Scott
  | publisher=University of Nebraska–Lincoln
  | date=1999-04-23
  | accessdate=2011-11-09 }}</ref>
* ''l'' is the length of the prongs in metres.
* ''E'' is the [[Young's modulus]] of the material the fork is made from in [[Pascal (unit)|pascal]]s.
* ''I'' is the [[second moment of area]] of the cross-section in metres to the fourth power.
* ''ρ'' is the [[density]] of the material the fork is made from in [[kilogramme]]s per cubic metre.
* ''A'' is the cross-sectional [[area]] of the prongs (tines) in square metres.


The ratio <math>\frac{I}{A}</math> in the equation above can be rewritten as
If all four resistor values and the supply voltage ({{math|''V''<sub>''S''</sub>}}) are known, and the resistance of the galvanometer is high enough that {{math|''I''<sub>''G''</sub>}} is negligible, the voltage across the bridge ({{math|''V''<sub>''G''</sub>}}) can be found by working out the voltage from each [[potential divider]] and subtracting one from the other. The equation for this is:
<math>r^2/4</math> if the prongs are cylindrical of radius ''r'', and
:<math>V_G = \left({{R_x}\over{R_3 + R_x}} - {{R_2}\over{R_1 + R_2}}\right)V_s</math>
<math>a^2/12</math> if the prongs have rectangular cross-section of width ''a'' along the direction of motion.


==Uses==
where {{math|''V''<sub>''G''</sub>}} is the voltage of node B relative to node D.
[[Image:Accutron.jpg|thumb|A [[Bulova]] Accutron watch from the 1960s, which uses a steel tuning fork ''(visible in center)'' vibrating at 360 Hz.]]
Forks have traditionally been used to [[Musical tuning|tune]] [[musical instrument]]s, although [[electronic tuner]]s are replacing them in many applications.  Tuning forks can be driven electrically, by placing [[electromagnet]]s close to the prongs that are attached to an [[electronic oscillator]] circuit, so that their sound does not die out.


===In musical instruments===
== Significance ==
A number of [[keyboard instrument|keyboard]] musical instruments using constructions similar to tuning forks have been made, the most popular of them being the [[Rhodes piano]], which has hammers hitting constructions working on the same principle as tuning forks and uses electric amplification of the generated sound. The earlier, unamplified [[dulcitone]] used tuning forks directly; it suffered from faintness of volume.


[[File:Inside QuartzCrystal-Tuningfork.jpg|thumb|right|Quartz crystal resonator from a modern [[quartz watch]], formed in the shape of a tuning fork.  It vibrates at 32,768 Hz in the [[ultrasound|ultrasonic]] range.]]
The Wheatstone bridge illustrates the concept of a difference measurement, which can be extremely accurate. Variations on the Wheatstone bridge can be used to measure [[capacitance]], [[inductance]], [[Electrical impedance|impedance]] and other quantities, such as the amount of combustible gases in a sample, with an [[explosimeter]]. The [[Kelvin bridge]] was specially adapted from the Wheatstone bridge for measuring very low resistances.  In many cases, the significance of measuring the unknown resistance is related to measuring the impact of some physical phenomenon (such as force, temperature, pressure, etc.) which thereby allows the use of Wheatstone bridge in measuring those elements indirectly.


===In clocks and watches===
The concept was extended to [[alternating current]] measurements by [[James Clerk Maxwell]] in 1865 and further improved by [[Alan Blumlein]] in about 1926.
The [[crystal oscillator|quartz crystal]] that serves as the timekeeping element in modern [[quartz clock]]s and [[watch]]es ''(right)'' is in the form of a tiny tuning fork.  It usually vibrates at a frequency of 32,768&nbsp;Hz in the [[ultrasound|ultrasonic]] range, above the range of human hearing.  It is made to vibrate by small oscillating voltages applied to metal electrodes plated on the surface of the crystal, by an [[electronic oscillator]] circuit. Quartz is [[piezoelectric]], so the voltage causes the fork tines to bend rapidly back and forth.


The [[Accutron]] ''(right)'', an [[Electromechanical watches|electromechanical watch]] developed by Max Hetzel and manufactured by [[Bulova]] beginning in 1960, used a 360 [[hertz]] steel tuning fork as its timekeeper, powered by electromagnets attached to a battery-powered transistor oscillator circuit.  The fork allowed it to achieve greater accuracy than conventional balance wheel watches.  The humming sound of the tuning fork could be heard when the watch was held to the ear.
==Modifications of the fundamental bridge==
[[File:Kelvin bridge by RFT.png|right|thumb|300px|[[Kelvin bridge]]]]
The Wheatstone bridge is the fundamental bridge, but there are other modifications that can be made to measure various kinds of resistances when the fundamental Wheatstone bridge is not suitable. Some of the modifications are:
* [[Carey Foster bridge]], for measuring small resistances
* [[Kelvin–Varley_divider|Kelvin Varley Slide]]
* [[Kelvin bridge]]
* [[Maxwell bridge]]


===Medical and scientific uses===
==See also==
[[Image:Tuning fork oscillator frequency standard.jpg|thumb|1 kHz tuning fork [[vacuum tube]] [[electronic oscillator|oscillator]] used by the U.S. National Bureau of Standards (now [[National Institute of Standards and Technology|NIST]]) in 1927 as a frequency standard.]]
{{Portal|Electronics}}
 
* [[Murray loop bridge]]
An alternative to the usual A440 diatonic scale is that of [[Concert pitch#19th and 20th century standards|philosophical or scientific pitch]] with standard pitch of C512. According to [[John William Strutt, 3rd Baron Rayleigh|Rayleigh]], the scale was used by physicists and acoustic instrument makers.<ref>{{cite book|last=Rayleigh|first=J.W.S.|title=The Theory of Sound|year=1945|publisher=Dover|location=New York|isbn=0-486-60292-3|page=9}}</ref> The tuning fork that John Shore gave to Handel gives a pitch of C512.<ref>[http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1291142/pdf/jrsocmed00168-0057.pdf The origin of the tuning fork - nih]</ref>
* [[Maxwell bridge]]
 
* [[Wien bridge]]
Tuning forks, usually C512, are used by medical practitioners to assess a patient's hearing. This is most commonly done with two exams called the [[Weber test]] and [[Rinne test]], respectively.  Lower-pitched ones (usually C128) are also used to check vibration sense as part of the examination of the peripheral nervous system.<ref>{{cite book |last1=Bickley |first1=Lynn |authorlink1= Lynn Bickley |last2=Szilagyi |first2=Peter |authorlink2=Peter Szilagyi |date=2009 |title=Bates' guide to the physical examination and history taking |edition=10th |location=Philadelphia, PA |publisher=Lippincott Williams & Wilkins |isbn=978-0-7817-8058-2}}</ref>
* [[Phantom circuit]] - a circuit using a balanced bridge
 
* [[Post Office Box (electricity)|Post Office Box]]
Tuning forks also play a role in several [[alternative medicine]] modalities, such as [[sonopuncture]] and [[polarity therapy]].
* [[Potentiometer]]
 
* [[Potential divider]]
=== Radar gun calibration ===
* [[Ohmmeter]]
A [[radar gun]], typically used for measuring the speed of cars or balls in sports, is usually calibrated with tuning forks.<ref>[http://tf.nist.gov/timefreq/general/pdf/87.pdf Calibration of Police Radar Instruments, National Bureau of Standards, 1976]</ref><ref>{{cite web
* [[Resistance thermometer]]
  | last =
* [[Strain gauge]]
  | first =
* [[E-meter]] - a variation used by [[Scientology]]
  | authorlink =
  | coauthors =
  | title = A detailed explanation of how police radars work
  | work = Radars.com.au
  | publisher = TCG Industrial, Perth, Australia
  | year = 2009
  | url = http://radars.com.au/police-radar.php
  | format =
  | doi =
  | accessdate = 2010-04-08}}</ref>
Instead of the frequency, these forks are labeled with the calibration speed and radar band (e.g. X-Band or K-Band) for which they are calibrated.
 
===In gyroscopes===
Doubled and H-type of tuning forks are used for tactical-grade [[Vibrating structure gyroscope#Tuning fork gyroscope|Vibrating Structure Gyroscopes]] like QuapasonTM and different types of MEMS.<ref>Proceedings of Anniversary Workshop on Solid-State Gyroscopy (19–21 May 2008. Yalta, Ukraine). - Kyiv-Kharkiv. ATS of Ukraine. 2009. - ISBN 978-976-0-25248-6 {{Please check ISBN|reason=Check digit (6) does not correspond to calculated figure.}}.</ref>
 
== See also ==
* [[Electronic tuner]]
* [[Pitch pipe]]
* [[Savart wheel]]
* [[Weber test]]
* [[Rinne test]]


==References==
==References==
{{reflist}}
<references/>


==External links==
==External links==
{{Commons category|Tuning forks}}
* [http://www.magnet.fsu.edu/education/tutorials/java/wheatstonebridge/index.html Wheatstone Bridge - Interactive Java Tutorial] National High Magnetic Field Laboratory
*[http://www.onlinetuningfork.com/ Onlinetuningfork.com], an online tuning fork using [[Macromedia]] [[Flash Player]].
*[http://www.efunda.com/designstandards/sensors/methods/wheatstone_bridge.cfm efunda Wheatstone article]
*[http://www.usneurologicals.com/ Usneurologicals.com], numerous examples of medical uses of tuning forks.
*[http://books.google.com/books?id=z3lKAAAAMAAJ Methods of Measuring Electrical Resistance - Edwin F. Northrup, 1912, full-text on Google Books]
{{Use dmy dates|date=March 2011}}
*[http://www.strainmatics.com Measuring strain using Wheatstone bridge principles]


{{DEFAULTSORT:Tuning Fork}}
{{DEFAULTSORT:Wheatstone Bridge}}
[[Category:1711 introductions]]
[[Category:Electrical meters]]
[[Category:Musical instrument parts and accessories]]
[[Category:Electrical circuits]]
[[Category:Idiophones]]
[[Category:Measuring instruments]]
[[Category:English inventions]]
[[Category:Impedance measurements]]

Revision as of 06:56, 9 August 2014

A Wheatstone bridge has four resistors forming the sides of a diamond shape. A battery is connected across one pair of opposite corners, and a galvanometer across the other pair.
Wheatstone bridge circuit diagram.

A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer. It was invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. One of the Wheatstone bridge's initial uses was for the purpose of soils analysis and comparison.[1]

Operation

In the figure, is the unknown resistance to be measured; , and are resistors of known resistance and the resistance of is adjustable. If the ratio of the two resistances in the known leg is equal to the ratio of the two in the unknown leg , then the voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer . If the bridge is unbalanced, the direction of the current indicates whether is too high or too low. is varied until there is no current through the galvanometer, which then reads zero.

Detecting zero current with a galvanometer can be done to extremely high accuracy. Therefore, if , and are known to high precision, then can be measured to high precision. Very small changes in disrupt the balance and are readily detected.

At the point of balance, the ratio of

Alternatively, if , , and are known, but is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of , using Kirchhoff's circuit laws (also known as Kirchhoff's rules). This setup is frequently used in strain gauge and resistance thermometer measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.

Derivation

First, Kirchhoff's first rule is used to find the currents in junctions B and D:

Then, Kirchhoff's second rule is used for finding the voltage in the loops ABD and BCD:

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Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer., so the second set of equations can be rewritten as:

Then, the equations are divided and rearranged, giving:

From the first rule, Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

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This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. and Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer.. The desired value of Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. is now known to be given as:

If all four resistor values and the supply voltage (Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer.) are known, and the resistance of the galvanometer is high enough that Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. is negligible, the voltage across the bridge (Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer.) can be found by working out the voltage from each potential divider and subtracting one from the other. The equation for this is:

where Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. is the voltage of node B relative to node D.

Significance

The Wheatstone bridge illustrates the concept of a difference measurement, which can be extremely accurate. Variations on the Wheatstone bridge can be used to measure capacitance, inductance, impedance and other quantities, such as the amount of combustible gases in a sample, with an explosimeter. The Kelvin bridge was specially adapted from the Wheatstone bridge for measuring very low resistances. In many cases, the significance of measuring the unknown resistance is related to measuring the impact of some physical phenomenon (such as force, temperature, pressure, etc.) which thereby allows the use of Wheatstone bridge in measuring those elements indirectly.

The concept was extended to alternating current measurements by James Clerk Maxwell in 1865 and further improved by Alan Blumlein in about 1926.

Modifications of the fundamental bridge

Kelvin bridge

The Wheatstone bridge is the fundamental bridge, but there are other modifications that can be made to measure various kinds of resistances when the fundamental Wheatstone bridge is not suitable. Some of the modifications are:

See also

Sportspersons Hyslop from Nicolet, usually spends time with pastimes for example martial arts, property developers condominium in singapore singapore and hot rods. Maintains a trip site and has lots to write about after touring Gulf of Porto: Calanche of Piana.

References

  1. ↑ "The Genesis of the Wheatstone Bridge" by Stig Ekelof discusses Christie's and Wheatstone's contributions, and why the bridge carries Wheatstone's name. Published in "Engineering Science and Education Journal", volume 10, no 1, February 2001, pages 37–40.

External links

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