# 21.5 Null measurements

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• 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 $V$ , which is related to the emf of the battery by $V=\text{emf}-\text{Ir}$ , where $I$ is the current that flows and $r$ is the internal resistance of the battery.

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

A potentiometer    is a null measurement device for measuring potentials (voltages). (See [link] .) A voltage source is connected to a resistor $\mathrm{R,}$ say, a long wire, and passes a constant current through it. There is a steady drop in potential (an $\text{IR}$ 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 ${\text{emf}}_{x}$ (represented by script ${E}_{x}$ in the figure) connected in series with a galvanometer. Note that ${\text{emf}}_{x}$ 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, ${\text{emf}}_{x}={\text{IR}}_{x}$ , where ${R}_{x}$ 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 ${\text{emf}}_{x}$ is directly sensed.

Now, a very precisely known standard ${\text{emf}}_{s}$ is substituted for ${\text{emf}}_{x}$ , and the contact point is adjusted until the galvanometer again reads zero, so that ${\text{emf}}_{s}={\text{IR}}_{s}$ . In both cases, no current passes through the galvanometer, and so the current $I$ through the long wire is the same. Upon taking the ratio $\frac{{\text{emf}}_{x}}{{\text{emf}}_{s}}$ , $I$ cancels, giving

is there a formula for magnitudes of displacement
A Body of maas m slides down an incline and reached the bottoms with a velocity v
What is mass
mass is the amount of matter a body contains.
prakash
what is model
what is a dimension
John
When using the Conservation of Energy equation, do we substitute the energy as a negative quantity when the energies on a single object are exerting forces opposite to one another?
Ex. On an inclined plane, gravitational potential energy, friction energy/work and spring potential energy. (Let's say that the spring is keeping the box from sliding down the slope.) How do we use this in the equation? I'm so confused
Jennifer
Oh! And if there's kinetic energy that is exerting a force opposite to the spring, what do we do?
Jennifer
Then we subtract the k.e. from force exerted from newton's 2nd law.
Prem
Subtract energy from force? They're different units
Jennifer
why is it dat when using double pan balance the known and unknown mass are the same
discuss the uses of energy in the following sectors of economy security and education
amajuoyi
why the current produce during dc motot is not use for its working rather we have to supply current outside
Tanveer
is there more then 4 dimensions
hii
princy
hi
Miguel
hello I kinda need help in physics... a lot
Brown
Brown. what kind of help
Jeff
when it comes to physics stick with the basics don't overthink things
Jeff
yes
ayesha
sticking to the basics will take you farther than overwhelming yourself with more than you need to physics is simple keep it simple
Jeff
thk u Ayesha
Jeff
for real....? so I've got to know the fundamentals and use the formula to solve any problem
Brown
read Stephan hawkings a brief history of time
ayesha
ayesha
physics isn't hard it's just understanding and applying the formulas if u need help ask any question
ayesha
okay...because I've got an exam next year February a Computer based exam
Brown
ayesha
ayesha
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Varun
hello
Ibrahim
yeah
oyeronke
how can we find absolute uncertainty
it what?
Luke
in physics
ayesha
the basic formula is uncertainty in momentum multiplied buy uncertainty In position is greater than or equal to 4×pi/2. same formula for energy and time
Luke
I have this one question can you please look it up it's 9702/22/O/N/17 Question 1 B 3
ayesha
what
uma
would you like physics?
Suthar
yes
farooq
precision or absolute uncertainty is always equal to least count of that instrument
Iram
how do I unlock the MCQ and the Essay?
what is the dimension of strain
Is there a formula for time of free fall given that the body has initial velocity? In other words, formula for time that takes a downward-shot projectile to hit the ground. Thanks!
hi
Agboro
hiii
Chandan
Hi
Sahim
hi
Jeff
hey
Priscilla
sup guys
Bile
Hy
Kulsum
What is unit of watt?
Kulsum
watt is the unit of power
Rahul
p=f.v
Rahul
watt can also be expressed as Nm/s
Rahul
what s i unit of mass
Maxamed
SI unit of mass is Kg(kilogram).
Robel
what is formula of distance
Maxamed
Formula for for the falling body with initial velocity is:v^2=v(initial)^2+2*g*h
Mateo
i can't understand
Maxamed
we can't do this calculation without knowing the height of the initial position of the particle
Chathu
sorry but no more in science
Imoreh
2 forces whose resultant is 100N, are at right angle to each other .if one of them makes an angle of 30 degree with the resultant determine it's magnitude
50 N... (50 *1.732)N
Sahim
Plz cheak the ans and give reply..
Sahim
50 N...(50 *1.732)N
Ibrahim
show the working
usiomon
what is the value of f1 and f2
Syed
what is the value of force 1 and force 2.
Syed
.
Is earth is an inertial frame?
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system
Sahim
thanks
Irungu
Most welcome
Sahim
Hey.. I've a question.
Is earth inertia frame?
Sahim
only the center
Shii
What is an abucus?
Irungu
what would be the correct interrogation "what is time?" or "how much has your watch ticked?"
prakash
hmmmm
oyeronke
coming
oyeronke
time is the distance measured on clock
KINGSFORD
time is that in which events are distinguishable with reference to before and after
Omo
time measure of duration interval of period
Sewmeho
a load of 20N on a wire of cross sectional area 8×10^-7m produces an extension of 10.4m. calculate the young modules of the material of the wire is of length 5m
Young's modulus = stress/strain strain = extension/length (x/l) stress = force/area (F/A) stress/strain is F l/A x
El
so solve it
Ebenezer
Ebenezer