# 21.5 Null measurements  (Page 3/8)

 Page 3 / 8
${I}_{1}{R}_{1}={I}_{2}{R}_{3}.$

Again, since b and d are at the same potential, the $\text{IR}$ drop along dc must equal the $\text{IR}$ drop along bc. Thus,

${I}_{1}{R}_{2}={I}_{2}{R}_{\text{x}}.$

Taking the ratio of these last two expressions gives

$\frac{{I}_{1}{R}_{1}}{{I}_{1}{R}_{2}}=\frac{{I}_{2}{R}_{3}}{{I}_{2}{R}_{x}}.$

Canceling the currents and solving for R x yields

${R}_{\text{x}}={R}_{3}\frac{{R}_{2}}{{R}_{1}}.$

This equation is used to calculate the unknown resistance when current through the galvanometer is zero. This method can be very accurate (often to four significant digits), but it is limited by two factors. First, it is not possible to get the current through the galvanometer to be exactly zero. Second, there are always uncertainties in ${R}_{1}$ , ${R}_{2}$ , and ${R}_{3}$ , which contribute to the uncertainty in ${R}_{x}$ .

Identify other factors that might limit the accuracy of null measurements. Would the use of a digital device that is more sensitive than a galvanometer improve the accuracy of null measurements?

One factor would be resistance in the wires and connections in a null measurement. These are impossible to make zero, and they can change over time. Another factor would be temperature variations in resistance, which can be reduced but not completely eliminated by choice of material. Digital devices sensitive to smaller currents than analog devices do improve the accuracy of null measurements because they allow you to get the current closer to zero.

## Section summary

• Null measurement techniques achieve greater accuracy by balancing a circuit so that no current flows through the measuring device.
• One such device, for determining voltage, is a potentiometer.
• Another null measurement device, for determining resistance, is the Wheatstone bridge.
• Other physical quantities can also be measured with null measurement techniques.

## Conceptual questions

Why can a null measurement be more accurate than one using standard voltmeters and ammeters? What factors limit the accuracy of null measurements?

If a potentiometer is used to measure cell emfs on the order of a few volts, why is it most accurate for the standard ${\text{emf}}_{\text{s}}$ to be the same order of magnitude and the resistances to be in the range of a few ohms?

## Problem exercises

What is the ${\text{emf}}_{\text{x}}$ of a cell being measured in a potentiometer, if the standard cell’s emf is 12.0 V and the potentiometer balances for ${R}_{\text{x}}=5\text{.}\text{000}\phantom{\rule{0.15em}{0ex}}\Omega$ and ${R}_{\text{s}}=2\text{.}\text{500}\phantom{\rule{0.15em}{0ex}}\Omega$ ?

24.0 V

Calculate the ${\text{emf}}_{\text{x}}$ of a dry cell for which a potentiometer is balanced when ${R}_{\text{x}}=1\text{.}\text{200}\phantom{\rule{0.25em}{0ex}}\Omega$ , while an alkaline standard cell with an emf of 1.600 V requires ${R}_{\text{s}}=1\text{.}\text{247}\phantom{\rule{0.25em}{0ex}}\Omega$ to balance the potentiometer.

When an unknown resistance ${R}_{\text{x}}$ is placed in a Wheatstone bridge, it is possible to balance the bridge by adjusting ${R}_{3}$ to be $\text{2500}\phantom{\rule{0.25em}{0ex}}\Omega$ . What is ${R}_{\text{x}}$ if $\frac{{R}_{2}}{{R}_{1}}=0\text{.}\text{625}$ ?

$1\text{.}\text{56 k}\Omega$

To what value must you adjust ${R}_{3}$ to balance a Wheatstone bridge, if the unknown resistance ${R}_{\text{x}}$ is $\text{100}\phantom{\rule{0.15em}{0ex}}\Omega$ , ${R}_{1}$ is $\text{50}\text{.}0\phantom{\rule{0.15em}{0ex}}\Omega$ , and ${R}_{2}$ is $\text{175}\phantom{\rule{0.15em}{0ex}}\Omega$ ?

(a) What is the unknown ${\text{emf}}_{\text{x}}$ in a potentiometer that balances when ${R}_{\text{x}}$ is $\text{10}\text{.}0\phantom{\rule{0.15em}{0ex}}\Omega$ , and balances when ${R}_{\text{s}}$ is $\text{15}\text{.}0\phantom{\rule{0.15em}{0ex}}\Omega$ for a standard 3.000-V emf? (b) The same ${\text{emf}}_{\text{x}}$ is placed in the same potentiometer, which now balances when ${R}_{\text{s}}$ is $\text{15}\text{.}0\phantom{\rule{0.15em}{0ex}}\Omega$ for a standard emf of 3.100 V. At what resistance ${R}_{\text{x}}$ will the potentiometer balance?

(a) 2.00 V

(b) $9\text{.}\text{68}\phantom{\rule{0.25em}{0ex}}\Omega$

Suppose you want to measure resistances in the range from $\text{10}\text{.}0\phantom{\rule{0.25em}{0ex}}\Omega$ to $\text{10}\text{.}0 k\Omega$ using a Wheatstone bridge that has $\frac{{R}_{2}}{{R}_{1}}=2\text{.}\text{000}$ . Over what range should ${R}_{3}$ be adjustable?

$\text{Range = 5}\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\Omega \phantom{\rule{0.25em}{0ex}}\text{to}\phantom{\rule{0.25em}{0ex}}5\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{k}\Omega$

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!