<< Chapter < Page Chapter >> Page >

Learning objectives

By the end of this section, you will be able to:

  • Explain why a null measurement device is more accurate than a standard voltmeter or ammeter.
  • Demonstrate how a Wheatstone bridge can be used to accurately calculate the resistance in a circuit.

Standard measurements of voltage and current alter the circuit being measured, introducing uncertainties in the measurements. Voltmeters draw some extra current, whereas ammeters reduce current flow. Null measurements balance voltages so that there is no current flowing through the measuring device and, therefore, no alteration of the circuit being measured.

Null measurements are generally more accurate but are also more complex than the use of standard voltmeters and ammeters, and they still have limits to their precision. In this module, we shall consider a few specific types of null measurements, because they are common and interesting, and they further illuminate principles of electric circuits.

The potentiometer

Suppose you wish to measure the emf of a battery. Consider what happens if you connect the battery directly to a standard voltmeter as shown in [link] . (Once we note the problems with this measurement, we will examine a null measurement that improves accuracy.) As discussed before, the actual quantity measured is the terminal voltage V size 12{V} {} , which is related to the emf of the battery by V = emf Ir size 12{V="emf" - ital "Ir"} {} , where I size 12{I} {} is the current that flows and r size 12{r} {} is the internal resistance of the battery.

The emf could be accurately calculated if r size 12{r} {} were very accurately known, but it is usually not. If the current I size 12{I} {} could be made zero, then V = emf size 12{V="emf"} {} , and so emf could be directly measured. However, standard voltmeters need a current to operate; thus, another technique is needed.

The diagram shows equivalence between two circuits. The first circuit has a cell of e m f script E and an internal resistance r connected across a voltmeter. The equivalent circuit on the right shows the same cell of e m f script E and an internal resistance r connected across a series combination of a galvanometer with an internal resistance r sub G and high resistance R. The currents in the two circuits are shown to be equal.
An analog voltmeter attached to a battery draws a small but nonzero current and measures a terminal voltage that differs from the emf of the battery. (Note that the script capital E symbolizes electromotive force, or emf.) Since the internal resistance of the battery is not known precisely, it is not possible to calculate the emf precisely.

A potentiometer    is a null measurement device for measuring potentials (voltages). (See [link] .) A voltage source is connected to a resistor R, say, a long wire, and passes a constant current through it. There is a steady drop in potential (an IR size 12{ ital "IR"} {} drop) along the wire, so that a variable potential can be obtained by making contact at varying locations along the wire.

[link] (b) shows an unknown emf x size 12{"emf" rSub { size 8{x} } } {} (represented by script E x size 12{"emf" rSub { size 8{x} } } {} in the figure) connected in series with a galvanometer. Note that emf x size 12{"emf" rSub { size 8{x} } } {} opposes the other voltage source. The location of the contact point (see the arrow on the drawing) is adjusted until the galvanometer reads zero. When the galvanometer reads zero, emf x = IR x size 12{"emf" rSub { size 8{x} } = ital "IR" rSub { size 8{x} } } {} , where R x size 12{R rSub { size 8{x} } } {} is the resistance of the section of wire up to the contact point. Since no current flows through the galvanometer, none flows through the unknown emf, and so emf x size 12{"emf" rSub { size 8{x} } } {} is directly sensed.

Now, a very precisely known standard emf s size 12{"emf" rSub { size 8{s} } } {} is substituted for emf x size 12{"emf" rSub { size 8{x} } } {} , and the contact point is adjusted until the galvanometer again reads zero, so that emf s = IR s size 12{"emf" rSub { size 8{s} } = ital "IR" rSub { size 8{s} } } {} . In both cases, no current passes through the galvanometer, and so the current I size 12{I} {} through the long wire is the same. Upon taking the ratio emf x emf s size 12{ { {"emf" rSub { size 8{x} } } over {"emf" rSub { size 8{s} } } } } {} , I size 12{I} {} cancels, giving

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 5

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask