Meter Bridge: Finding Error in Resistance

AI Thread Summary
The discussion focuses on finding the error in resistance measurements using a meter bridge. Participants explore methods to calculate resistance and its associated error, emphasizing the importance of the reading error, which can be defined as either the smallest scale or half of it. Calculations are demonstrated with specific values, showing how slight changes in the slide contact position affect resistance readings. The derivative method is suggested as a more precise approach to determine resistance error, reinforcing the relationship between reading error and resistance deviation. Overall, the conversation clarifies how to quantify measurement errors in resistance using different techniques.
LoveBoy
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Homework Statement


Q0lRdWc.png


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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Likes LoveBoy
I got it now !
Thanks for your help @ehild :wink:
 
You are welcome.
 

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