<< 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

I'm interested in biological psychology and cognitive psychology
Tanya Reply
what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
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