<< Chapter < Page Chapter >> Page >
I 1 R 1 = I 2 R 3 . size 12{I rSub { size 8{1} } R rSub { size 8{1} } =I rSub { size 8{2} } R rSub { size 8{3} } } {}

Again, since b and d are at the same potential, the IR size 12{ ital "IR"} {} drop along dc must equal the IR size 12{ ital "IR"} {} drop along bc. Thus,

I 1 R 2 = I 2 R x . size 12{I rSub { size 8{1} } R rSub { size 8{2} } =I rSub { size 8{2} } R rSub { size 8{x} } } {}

Taking the ratio of these last two expressions gives

I 1 R 1 I 1 R 2 = I 2 R 3 I 2 R x . size 12{ { {I rSub { size 8{1} } R rSub { size 8{1} } } over {I rSub { size 8{1} } R rSub { size 8{2} } } } = { {I rSub { size 8{2} } R rSub { size 8{3} } } over {I rSub { size 8{2} } R rSub { size 8{x} } } } } {}

Canceling the currents and solving for R x yields

R x = R 3 R 2 R 1 . size 12{R rSub { size 8{x} } =R rSub { size 8{3} } { {R rSub { size 8{2} } } over {R rSub { size 8{1} } } } } {}
This complex circuit diagram shows a galvanometer connected in the center arm of a Wheatstone bridge arrangement. All the other four arms have a resistor. The bridge is connected to a cell of e m f script E and internal resistance r.
The Wheatstone bridge is used to calculate unknown resistances. The variable resistance R 3 size 12{R rSub { size 8{3} } } {} is adjusted until the galvanometer reads zero with the switch closed. This simplifies the circuit, allowing R x size 12{R rSub { size 8{x} } } {} to be calculated based on the IR size 12{ ital "IR"} {} drops as discussed in the text.

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 size 12{R rSub { size 8{1} } } {} , R 2 size 12{R rSub { size 8{2} } } {} , and R 3 size 12{R rSub { size 8{3} } } {} , which contribute to the uncertainty in R x size 12{R rSub { size 8{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.

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

If a potentiometer is used to measure cell emfs on the order of a few volts, why is it most accurate for the standard emf s size 12{"emf" rSub { size 8{s} } } {} to be the same order of magnitude and the resistances to be in the range of a few ohms?

Got questions? Get instant answers now!

Problem exercises

What is the emf x size 12{"emf" rSub { size 8{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 x = 5 . 000 Ω size 12{R rSub { size 8{x} } =5 "." "000" %OMEGA } {} and R s = 2 . 500 Ω size 12{R rSub { size 8{s} } =2 "." "500" %OMEGA } {} ?

24.0 V

Got questions? Get instant answers now!

Calculate the emf x size 12{"emf" rSub { size 8{x} } } {} of a dry cell for which a potentiometer is balanced when R x = 1 . 200 Ω size 12{R rSub { size 8{x} } =1 "." "200" %OMEGA } {} , while an alkaline standard cell with an emf of 1.600 V requires R s = 1 . 247 Ω size 12{R rSub { size 8{s} } =1 "." "247" %OMEGA } {} to balance the potentiometer.

Got questions? Get instant answers now!

When an unknown resistance R x size 12{R rSub { size 8{x} } } {} is placed in a Wheatstone bridge, it is possible to balance the bridge by adjusting R 3 size 12{R rSub { size 8{3} } } {} to be 2500 Ω size 12{"2500" %OMEGA } {} . What is R x size 12{R rSub { size 8{x} } } {} if R 2 R 1 = 0 . 625 size 12{ { {R rSub { size 8{2} } } over {R rSub { size 8{1} } } } =0 "." "625"} {} ?

1 . 56 k Ω size 12{1 "." "56 k" %OMEGA } {}

Got questions? Get instant answers now!

To what value must you adjust R 3 size 12{R rSub { size 8{3} } } {} to balance a Wheatstone bridge, if the unknown resistance R x size 12{R rSub { size 8{x} } } {} is 100 Ω size 12{"100" %OMEGA } {} , R 1 size 12{R rSub { size 8{1} } } {} is 50 . 0 Ω size 12{"50" "." 0 %OMEGA } {} , and R 2 size 12{R rSub { size 8{2} } } {} is 175 Ω size 12{"175" %OMEGA } {} ?

Got questions? Get instant answers now!

(a) What is the unknown emf x size 12{"emf" rSub { size 8{x} } } {} in a potentiometer that balances when R x size 12{R rSub { size 8{x} } } {} is 10 . 0 Ω size 12{"10" "." 0 %OMEGA } {} , and balances when R s size 12{R rSub { size 8{s} } } {} is 15 . 0 Ω size 12{"15" "." 0 %OMEGA } {} for a standard 3.000-V emf? (b) The same emf x size 12{"emf" rSub { size 8{x} } } {} is placed in the same potentiometer, which now balances when R s size 12{R rSub { size 8{s} } } {} is 15 . 0 Ω size 12{"15" "." 0 %OMEGA } {} for a standard emf of 3.100 V. At what resistance R x size 12{R rSub { size 8{x} } } {} will the potentiometer balance?

(a) 2.00 V

(b) 9 . 68 Ω size 12{9 "." "68 " %OMEGA } {}

Got questions? Get instant answers now!

Suppose you want to measure resistances in the range from 10 . 0 Ω size 12{"10" "." 0 %OMEGA } {} to 10 . 0 kΩ size 12{"10" "." 0" k" %OMEGA } {} using a Wheatstone bridge that has R 2 R 1 = 2 . 000 size 12{ { {R rSub { size 8{2} } } over {R rSub { size 8{1} } } } =2 "." "000"} {} . Over what range should R 3 size 12{R rSub { size 8{3} } } {} be adjustable?

Range = 5 . 00 Ω to 5 . 00 k Ω size 12{"Range=5" "." "00 " %OMEGA " to "5 "." "00"" k" %OMEGA } {}
Got questions? Get instant answers now!

Questions & Answers

a 50kg mass is placed on a frictionless piston fitted to a gas cylinder .If 149 kelvin of heat is supplied to the cylinder increasing the internal energy by 100 joules,determine the height through which the mass of the piston raise
Lawal Reply
what is thermodynamics
wana Reply
thermodynamic is a branch of physics that teaches on the relationship about heat and anyother form of energy
Emmanuel
could you please help solve question on thermodynamics
Lawal
if a mass of 149 of heat is supplied and there's an increase in internal energy of 100jouls,find the raise in height
Lawal
if l cary box and stop is ther any work
Tamirat Reply
no that because u have moved no distance. for work to be performed a force needs to be applied and a distance needs to be moved
Emmanuel
Different between fundamental unit and derived unit
Alimi Reply
fundamental unit are independent quantities that do not depend on any other unit while derived unit are quantities that depend on two or more units for it definition
Emmanuel
what is nuclear fission
Sadik Reply
hello
Shawty
are you there
Shawty
miss your absence here...
Shawty
what is a vector
Temitayo Reply
vectors are quantities that have numerical value or magnitude and direction.
Muhammad
what is regelation
Oladele
vector is any quantity that has magnitude and direction
Emmanuel
Physics is a physical science that deals with the study of matter in relation to energy
Divine Reply
Hi
Jimoh
hello
Salaudeen
hello
Sadik
Yes
Maxamuud
hi everyone
Muhammad
what is physics
Rhema Reply
physics is a physical science that deals with the study of matter in relation to energy
Osayuwa
a15kg powerexerted by the foresafter 3second
Firdos Reply
what is displacement
Xolani Reply
movement in a direction
Jason
hello
Hosea
Hey
Smart
haider
Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation? can someone please explain this i need it for my final exam
anas Reply
Hi
saeid
hi
Yimam
Hi
Jimoh
An object made of several thin conducting layers separated by insulation may not be affected by magnetic damping because the eddy current produced in each layer due to induction will be very small and the opposing magnetic flux produced by the eddy currents will be very small
Muhammad
What is thê principle behind movement of thê taps control
Oluwakayode Reply
while
Hosea
what is atomic mass
thomas Reply
this is the mass of an atom of an element in ratio with the mass of carbon-atom
Chukwuka
show me how to get the accuracies of the values of the resistors for the two circuits i.e for series and parallel sides
Jesuovie Reply
Explain why it is difficult to have an ideal machine in real life situations.
Isaac Reply
tell me
Promise
what's the s . i unit for couple?
Promise
its s.i unit is Nm
Covenant
Force×perpendicular distance N×m=Nm
Oluwakayode
İt iş diffucult to have idêal machine because of FRİCTİON definitely reduce thê efficiency
Oluwakayode
It is difficult to have an ideal machine in real life situation because in ideal machines all the input energy should be converted to output energy . But , some part of energy is always lost in overcoming friction and input energy is always greater than output energy . Hence , no machine is ideal.
Muhammad
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. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask