Meter Bridge: Finding Error in Resistance

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Homework Help Overview

The discussion revolves around determining the error in resistance measurements using a meter bridge setup. Participants explore how to quantify the uncertainty in resistance values based on the position of a slide contact and the associated reading errors.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss methods for calculating resistance and its error, including the use of derivatives and reading adjustments. Questions arise regarding the interpretation of deviations in resistance values and the significance of reading errors.

Discussion Status

The conversation includes various approaches to calculating resistance errors, with some participants suggesting different methods for determining reading errors. There is acknowledgment of the impact of reading errors on resistance calculations, but no consensus has been reached on a single method.

Contextual Notes

Participants mention specific reading errors (e.g., ±0.1 cm) and how these affect resistance calculations. There is a discussion on whether to consider the smallest scale or half of it as the reading error, indicating a lack of uniformity in assumptions.

LoveBoy
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Homework Statement


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Homework Equations


How to find error in resistance ?

The Attempt at a Solution


I found out the resistance without error.
But What is the way to figure out an error of an instrument ?
 
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Write the formula you use to calculate the unknown resistance. You read the position x of the slide contact with error of dx= 0.1 cm (or 0.05 cm). R is a function of x: R=f(x) and its error is dR=f ' (x) dx.
Some people consider the reading error as the smallest scale, other consider half of it as the reading error.
If you do not want to differentiate, calculate the resistance with the reading changed by ± the reading error. If it is ±1 mm, calculate the resistances with x=36.1cm and 35.9 cm, and give the deviation from the resistance calculated with x=36 cm.
 
ehild said:
Write the formula you use to calculate the unknown resistance. You read the position x of the slide contact with error of dx= 0.1 cm (or 0.05 cm). R is a function of x: R=f(x) and its error is dR=f ' (x) dx.
Some people consider the reading error as the smallest scale, other consider half of it as the reading error.
If you do not want to differentiate, calculate the resistance with the reading changed by ± the reading error. If it is ±1 mm, calculate the resistances with x=36.1cm and 35.9 cm, and give the deviation from the resistance calculated with x=36 cm.
As per your given hint,
i calculated resistance.
When x=36.1 cm , R=9.03 ohm
When x=35.9 cm, R=8.96 ohm

ehild said:
give the deviation from the resistance calculated with x=36 cm.
What does that mean ?
 
LoveBoy said:
As per your given hint,
i calculated resistance.
When x=36.1 cm , R=9.03 ohm
When x=35.9 cm, R=8.96 ohmWhat does that mean ?
You got 9 ohm with x=36. So the reading error makes the resistance value deviate about 0.3-04 ohm from the real one. To which answers is it closest?
I suggest to apply the other method, taking the derivative of R=f(x) and multiplying it with the reading error.
 
T5OhaS2.png

Right ?
 
LoveBoy said:
T5OhaS2.png

Right ?
If l is the length read on the meter, it is right. Take the derivative with respect to l at l=36 cm and multiplied it with Δl=0.1.
It is possible that the error of the reading is considered half of that, then the error of the resistance is also halved.
 
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I got it now !
Thanks for your help @ehild :wink:
 
You are welcome.
 

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