What is the most likely value of the current, with its uncertainty?

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In summary: Thanks a lot. I have done the part you suggested as my (a) solution. Its (b) that I will like further assistance.In summary, the manufacturer of a digital ammeter quotes its uncertainty as plus-minus 1.5% plus-minus 2 digits, which means adding 2 of the least significant digits to 1.5% of the measured value. For a constant reading of 2.64A, the uncertainty is plus-minus 0.06A. In part (b), the current fluctuates randomly between 1.58A and 2.04A, giving a range of 0.46A. To determine the most likely value of the current, its uncertainty must be taken into account using
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aurao2003
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Homework Statement


Hi
I need some help with this problem. It reads this way:
The manufacturer of a digital ammeter quotes its uncertainty as plus-minus 1.5% plus-minus 2 digits.

a) Determine the uncertainty in a constant reading of 2.64A
b) The meter is used to measure the current from a d.c power supply. The current is found to fluctuate randomly between 1.58A and 2.04A. Determine the most likely value of the current, with its uncertainty.



Homework Equations


uncertainty as plus-minus 1.5% plus-minus 2 digits.





The Attempt at a Solution


Solving (a)
2.64 x 1.5% = 0.0396
1.5% x 2 = 0.03
Adding the above =0.0696
The answer in my physics book is plus - minus 0.06A. Can anyone kindly clarify way? I know the number of significant figures determines the uncertainty. Can the answer not be 0.07A? (After rounding up)

Solving (b)
I am not sure how to being. Since uncertainty is the range of values, I decided to find the range
So, 2.04-1.58 = 0.46A

But not sure how to progress further. Any suggestions? (Please bear in mind I study independently)
 
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  • #2
The uncertainty quoted doesn't make much sense to me. Can you indicate exactly what was written? Did it really say exactly this:

± 1.5% ± 2 digits

or did you modify it in some way?
 
  • #3


cepheid said:
The uncertainty quoted doesn't make much sense to me. Can you indicate exactly what was written? Did it really say exactly this:

± 1.5% ± 2 digits

or did you modify it in some way?
Yes.Its correct (Advanced level Practical work for Physics, Chapter 1, p7- M Crundell & C Mee)
 
  • #4
I couldn't find anywhere that had even a preview of the inside of that book, but Googling the phrase "± 1.5% ± 2 digits"

let me to this datasheet for an actual digital multimeter:

http://www.bstcaltek.com/catalog/download/manual/1801_M.pdf

If you look above the table of electrical specifications in section 3.2 on that PDF document, there is a note that says:

Accuracies are ± (% of reading + number of least significant digits)

So this explains what your book is talking about. "2 digits" actually means "2 of the least significant digits", which means, "add two units of whatever the smallest digit in your measurement is."

In this case, the precision of your measurement is to the nearest hundredth of an amp, which means that after calculating 1.5% of the measured value, you add 2*0.01 to that. The least significant digit is in the hundredth's place in this example. So you add two hundredths of an amp. If you do that, you'll get something close to 0.06 A.
 
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  • #5
cepheid said:
I couldn't find anywhere that had even a preview of the inside of that book, but Googling the phrase "± 1.5% ± 2 digits"

let me to this datasheet for an actual digital multimeter:

http://www.bstcaltek.com/catalog/download/manual/1801_M.pdf

If you look above the table of electrical specifications in section 3.2 on that PDF document, there is a note that says:



So this explains what your book is talking about. "2 digits" actually means "2 of the least significant digits", which means, "add two units of whatever the smallest digit in your measurement is."

In this case, the precision of your measurement is to the nearest hundredth of an amp, which means that after calculating 1.5% of the measured value, you add 2*0.01 to that. The least significant digit is in the hundredth's place in this example. So you add two hundredths of an amp. If you do that, you'll get something close to 0.06 A.
Thanks a lot. I have done the part you suggested as my (a) solution. Its (b) that I will like further assistance.
 
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FAQ: What is the most likely value of the current, with its uncertainty?

What is uncertainty in a reading?

Uncertainty in a reading refers to the degree of error or imprecision associated with a measurement or observation. It is a measure of how much confidence we have in the accuracy of the data being collected.

How is uncertainty calculated?

Uncertainty is typically calculated by taking into account various sources of error, such as instrument precision, human error, and external factors. This can be done through statistical analysis, using tools such as standard deviation or confidence intervals.

Why is it important to consider uncertainty in scientific research?

Uncertainty is important to consider in scientific research because it allows us to understand the limitations of our data and the potential for error. Without acknowledging and accounting for uncertainty, our conclusions and findings may not be accurate or reliable.

How can uncertainty impact the interpretation of results?

Uncertainty can impact the interpretation of results by introducing doubt and potential bias into our conclusions. It can also affect the precision and accuracy of our measurements, leading to incorrect assumptions or conclusions.

What are some ways to reduce uncertainty in a reading?

There are several ways to reduce uncertainty in a reading, such as improving the precision and accuracy of instruments, minimizing human error through proper training and techniques, and controlling external factors that may affect the measurement. Additionally, taking multiple readings and averaging them can help reduce uncertainty.

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